ZAG Handbook of Algebraic Geometry provides an expansive collection of extended summaries of all the research talks given at the worldwide ZAG (Zoom Algebraic Geometry) Seminar as well as contributed short notes. Constructed from contributions from 2020-24 by active research algebraic geometers from all continents, the book is aimed at researchers in algebraic geometry and related fields who want to gain a comprehensive understanding of state-of-the-art research in algebraic geometry. The book is extensive and wide-ranging, and offers material suitable to multiple levels of readership: from advanced undergraduate students in mathematics to active specialised researchers.
Features
? A showcase of the most important worldwide trends in algebraic geometry in recent years
? Over two hundred short summaries of state-of-the-art research in algebraic geometry accessible to other mathematicians
? A combination of contributions by renowned mathematicians, key researchers and new talent
? Links to recordings of hour-long presentations for each contribution
Ivan Cheltsov is a Professor at the University of Edinburgh, United Kingdom, and his research interests include birational geometry and K-stability of Fano varieties. He is the author of 3 books and 126 articles written together with 52 co-authors. Ivan has organized research meetings in Auckland, Beijing, Cambridge, Durham, Edinburgh, Fuerteventura, Istanbul, Levico Terme, London, Magadan, Melbourne, Moscow, New York, Oberwolfach, Pipa, Pohang, Easter Island, Shanghai, Sochi, Spitsbergen, Stony Brook, Sydney, Tianjin, Wakkanai, and Vladivostok. Since 1995, Ivan has been married to Elena Cheltsova: they have three children (Ivan, Fedor, Ekaterina) and a cat, Kuzya. Aside from Mathematics, Ivan enjoys traveling, reading, and cycling his Brompton bicycle.
Jesus Martinez-Garcia is a Senior Lecturer in Pure Mathematics at the University of Essex, United Kingdom. He obtained his PhD at the University of Edinburgh in 2013 and has held research positions at the University of Bath, United Kingdom, Johns Hopkins University, United States, and the Max Planck Institute for Mathematics, Germany. His research is in algebraic geometry with special emphasis on birational geometry, moduli spaces, K-stability, Fano varieties, and computational algebraic geometry. Martinez-Garcia has written one book, several research articles, and two software packages, and he has co-organized more than ten research meetings, including the annual international conference AGGITatE, as well as several research seminars.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Postgraduate
Illustrationen
17 s/w Zeichnungen, 17 s/w Abbildungen
17 Line drawings, black and white; 17 Illustrations, black and white
Maße
Höhe: 254 mm
Breite: 178 mm
Gewicht
ISBN-13
978-1-032-26046-4 (9781032260464)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Ivan Cheltsov is Professor at the University of Edinburgh, and his research interests include birational geometry and K-stability of Fano varieties. He is author of 3 books and 126 papers written together with 52 co-authors. Ivan has organized research meetings in Auckland, Beijing, Cambridge, Durham, Edinburgh, Fuerteventura, Istanbul, Levico Terme, London, Magadan, Melbourne, Moscow, New York, Oberwolfach, Pipa, Pohang, Easter Island, Shanghai, Sochi, Spitsbergen, Stony Brook, Sydney, Tianjin, Wakkanai, Vladivostok. Since 1995, Ivan is married to Elena Cheltsova: they have three children (Ivan, Fedor, Ekaterina) and cat Kuzya. Aside of Mathematics, Ivan enjoys traveling, reading and cycling his Brompton bicycle.
Jesus Martinez-Garcia is Senior Lecturer in Pure Mathematics at the University of Essex (UK). He obtained his PhD at the University of Edinburgh in 2013 and has held research positions at the University of Bath (UK), Johns Hopkins University (US) and the Max Planck Institute for Mathematics (Germany). His research is in algebraic geometry with special emphasis on birational geometry, moduli spaces, K-stability, Fano varieties and computational algebraic geometry. Martinez-Garcia has written one book, several research articles and two software packages and he has co-organised more than 10 research meetings, including the annual international conference AGGITatE as well as several research seminars.
Table of Contents
1. Algebraic geometry in the times of Covid
Ivan Cheltsov and Jesus Martinez-Garcia
2. Models of Fano 3-folds
Hamid Abban
3. Weighted Ehrhart polynomials and series for the standard simplex
Praise Adeyemo
4. Advances in moduli theory
Jarod Alper
5. Normal form of a holomorphic Lagrangian submanifold
Ekaterina Amerik
6. Koszul modules and applications
Marian Aprodu
7. Euler characteristics of aspherical Kaehler manifolds
Donu Arapura
8. Birational geometry of Calabi-Yau pairs and Cremona transformations
Carolina Araujo
9. Enumerating punctured log maps via wall-crossing
Hulya Arguz
10. Biregular and birational geometry of rational nodal quartic double solids
Artem Avilov
11. Chern character of quantizable sheaves
Vladimir Baranovsky and Victor Ginzburg
12. Vector bundles on Fano threefolds and K3 surfaces
Arnaud Beauville
13. Cylinders in Del Pezzo surfaces with Du Val singularities
Grigory Belousov
14. Approximation of differentiable submanifolds by real algebraic subvarieties
Olivier Benoist
15. Kaehler-Einstein metrics, Archimedean zeta functions and phase transitions
Robert Berman
16. Geometry of 3-dimensional Del Pezzo fibrations in positive characteristic
Fabio Bernasconi
17. Geometry of polarised varieties
Caucher Birkar
18. On properness of K-moduli spaces and optimal destabilizations
Harold Blum
19. Surface with ample canonical bundle and Kuranishi space a nonreduced point
Christian Boehning
20. Projective geometry approach to the Jacobian conjecture
Alexander Borisov
21. Explicit equations of surfaces of general type
Lev Borisov
22. General type results for moduli of hyperkaehler varieties
Emma Brakkee
23. Geometric structures on spaces of quadratic differentials
Tom Bridgeland
24. Extending Tom and Jerry for Fano 3-folds
Gavin Brown, Stephen Coughlan and Tom Ducat
25. Supercycles and stable supermaps
Ugo Bruzzo and Daniel Hernandez Ruiperez
26. Arcs and singularities
Nero Budur
27. Chern-Weil theory and Hilbert-Samuel theorem for semipositive singular toroidal metrics
Jose Ignacio Burgos Gil
28. Index 2 Fano 3-folds and double covers
Livia Campo
29. Uniqueness of enhancements of triangulated categories
Alberto Canonaco, Amnon Neeman and Paolo Stellari
30. On the birational geometry of foliations
Paolo Cascini
31. Effective cones of moduli spaces of stable rational curves and blown up toric surfaces Ana-Maria Castravet
32. Nodal surfaces, coding theory, and cubic discriminants
Fabrizio Catanese
33. The minimal model program for arithmetic surfaces enriched by a Brauer class
Daniel Chan
34. Low dimensional components in the K-moduli of smoothable Fano 3-folds
Ivan Cheltsov
35. Remarks on n-folds of type (1,n)
Jungkai Chen
36. Singularities on toric fibrations
Yifei Chen and Caucher Birkar
37. On the distribution of canonical volumes and moduli spaces of varieties of general type
Meng Chen
38. Subadditivity theorem for Okounkov bodies
Sung Rak Choi
39. Enumeration of Terracini schemes
Ciro Ciliberto
40. Numerical characterization of complex torus quotients
Benoit Claudon
41. Slope inequalities and ample cone of KSB moduli spaces
Giulio Codogni
42. The cohomology of the moduli space of sheaves on surfaces
Izzet Coskun
43. Orbifold quot schemes via the le Bruyn-Procesi theorem
Alastair Craw
44. On quadratic points on intersections of two quadrics
Brendan Creutz and Bianca Viray
45. Deformations of exterior differential ideals and applications
Fernando Cukierman
46. Log minimal model program for Kaehler 3-folds
Omprokash Das
47. CSCK metrics on rank one spherical Fano fourfolds
Thibaut Delcroix
48. K-stability of P^3 blown up along the disjoint union of a twisted cubic curve and a line
Elena Denisova
49. Stability of fibrations
Ruadhai Dervan
50. Wall crossing for K-moduli spaces of plane curves
Kristin DeVleming
51. The bottleneck degree of algebraic varieties
Sandra Di Rocco
52. Dynamical filtrations|
Tien-Cuong Dinh, Hsueh-Yung Lin, Keiji Oguiso and De-Qi Zhang
53. Roth's theorem for adelic curves
Paolo Dolce and Francesco Zucconi
54. Enumerative geometry, fredholm analysis and moduli spaces of surfaces of general type Simon Donaldson
55. Bounding the complexity of 2-loop Feynman integrals
Charles Doran
56. K-stability of P^3 blown up along smooth curves of genus 4 and degree 6
Tiago Duarte Guerreiro
57. Rigidity of affine Brieskorn-Pham threefolds
Adrien Dubouloz
58. Birational geometry and cylindricity of Severi-Brauer varieties
Adrien Dubouloz, Kento Fujita, Takashi Kishimoto and Takuzo Okada
59. Okawa's theorem and wide subcategories of coherent sheaves on curves
Alexey Elagin
60. Mixed Hodge structure decomposition of alexander modules into generalized eigenspaces
Eva Elduque
61. Local stability threshold of Del Pezzo surfaces of degree 2
Erroxe Etxabarri Alberdi
62. Rational simple connectedness and the quintic Del Pezzo threefold
Andrea Fanelli
63. K3 structures from singular Fano varieties
Enrico Fatighenti
64. An overview of homotopy path algebras
David Favero
65. Quasi-invariants and free arrangements
Misha Feigin
66. The Brasselet-Schurmann-Yokura conjecture on L-classes of singular varieties
Javier Fernandez de Bobadilla and Irma Pallares Torres
67. Notes on motivic integration on Berkovich spaces
Tommaso de Fernex
68. Counting sheaves by counting curves
Soheyla Feyzbakhsh and Richard Thomas
69. On the boundedness of elliptically fibered Calabi-Yau threefolds
Stefano Filipazzi
70. Connected algebraic groups acting on Fano fibrations over P^1
Enrica Floris
71. Maximal automorphism groups of surfaces
Pascal Fong and Matilde Maccan
72. A canonical Hodge theoretic projective structure on compact Riemann surfaces
Paola Frediani
73. On extremal contractions of log canonical pairs
Osamu Fujino
74. On the singular loci of higher secant varieties of Veronese embeddings
Katsuhisa Furukawa
75. The Bourbaki degree of a plane curve
Daniel Futata and Marcos Jardim
76. Compactifications of the moduli space of marked cubic surfaces
Patricio Gallardo
77. Intrinsic mirrors for minimal adjoint orbits
Elizabeth Gasparim
78. On a generalized Batyrev's cone conjecture
Yoshinori Gongyo
79. Complex curves in hypercomplex nilmanifolds
Iulia Gorginian
80. Projective flatness over Klt spaces and characterisation of finite quotients of projective spaces
Daniel Greb
81. Distinguishing triangle-free level-one phylogenetic networks using computational algebraic geometry
Elizabeth Gross
82. Open FJRW theory and mirror symmetry: a ZAG lecture
Mark Gross, Tyler Kelly and Ran Tessler
83. Recent progress in the MMP for 3-folds and 4-folds in char p>0
Christopher Hacon
84. Rationality questions on Seshadri constants
Krishna Hanumanthu
85. Log symplectic pairs and mixed Hodge structures
Andrew Harder
86. Gaps between lc pairs and Klt pairs in a viewpoint of the minimal model theory
Kenta Hashizume
87. Constructing new Q-Fano threefolds using Laurent inversion
Liana Heuberger
88. Fano manifolds such that the tangent bundle is (not) big
Andreas Hoering
89. Geometric extension
Chris Hone and Geordie Williamson
90. An algebro-geometric higher Szemeredi lemma
Ehud Hrushovski
91. A dynamical approach to generalized Weil's Riemann hypothesis and semisimplicity Fei Hu
92. Torelli problem on logarithmic sheaves
Sukmoon Huh
93. Minimal rational curves and 1-flat cone structures
Jun-Muk Hwang
94. A bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds
Shihoko Ishii
95. The McKay correspondence
Yukari Ito
96. Shafarevich's conjecture for canonically polarized varieties revisited
Ariyan Javanpeykar, Steven Lu, Ruiran Sun and Kang Zuo
97. Symmetries of Fano varieties
Lena Ji
98. Minimal log discrepancies in dimension three
Chen Jiang
99. Equilateral convex triangulations of RP^2 with three conical points of equal defec
Nikita Kalinin
100. 1-dimensional K-moduli spaces of Fano 3-folds
Anne-Sophie Kaloghiros
101. A brief survey on stability of tangent bundles on Fano manifolds
Akihiro Kanemitsu
102. Are Klt Fano varieties of small volume stably rational?
Ilya Karzhemanov
103. New examples of surgery invariant counts in real algebraic geometry
Slava Kharlamov
104. Hodge sheaves for singular families
Sandor Kovacs
105. Secant varieties of real curves
Mario Kummer
106. Sextic double solids
Alexandra Kuznetsova
107. On effective cones of rational surfaces
Antonio Laface
108. The rational chow rings of M_7, M_8 and M_9
Hannah Larson
109. A Neron-Ogg-Shafarevich criterion for K3 surfaces
Chris Lazda
110. Derived categories and motives of moduli spaces of vector bundles on curves
Kyoung-Seog Lee
111. Dominant rational maps from a very general hypersurface
Yongnam Lee
112. Valuative stability of polarised varieties
Eveline Legendre
113. Rational curves on Del Pezzo surfaces in positive characteristic
Brian Lehmann
114. Codimension 2 cycles of classifying spaces of low-dimensional algebraic tori
Nicole Lemire
115. Locally free twisted sheaves of infinite rank
Max Lieblich
116. Rational curves on K3 surfaces
Christian Liedtke
117. Automorphisms of projective hypersurfaces
Alvaro Liendo
118. Motivic invariants of birational maps Hsueh-Yung Lin
Evgeny Shinder
119. A motivic version of topological mirror symmetry
Fransois Loeser
120. Poisson and symplectic geometry of the moduli spaces of Higgs bundles
Marina Logares
121. On non-rationality of degenerations of Del Pezzo surfaces
Konstantin Loginov
122. A conjecture on D algebras
Leonid Makar-Limanov
123. Fano threefolds of Picard rank 2 and volume 28
Joseph Malbon
124. Birational involutions of the real projective plane fixing an irrational curve
Frederic Mangolte
125. Unirationality of instanton moduli space for small charges
Dimitri Markushevich and Alexander Tikhomirov
126. The defect of a cubic threefold
Lisa Marquand
127. The determinant of cohomology and moduli of lambda-connections
Johan Martens
128. Two remarks on asymptotically log Fano pairs
Jesus Martinez-Garcia
129. On K-stability of Calabi-Yau fibrations
Hattori Masafumi
130. On the (uni)rationality problem for hypersurfaces
Alex Massarenti
131. Transformations of transfinite diameter
Sione Ma`u
132. Perverse-Hodge octahedron
Mirko Mauri
133. A special rational surface
Massimiliano Mella
134. On the top-weight rational cohomology of A_g
Margarida Melo
135. Jordan property for automorphism groups
Sheng Meng
136. Geometry and arithmetic of equivariant compactifications of the affine space
Pedro Montero
137. Special variational Hodge conjecture for toric varieties
William Montoya
138. Tropical geometry and phylogenetic diversity
Han-Bom Moon
139. Fundamental groups of singularities of the MMP
Joaquin Moraga
140. A moduli space in the differential geometry world
David Mumford
141. Interview with David Mumford
Ivan Cheltsov and Jesus Martinez-Garcia
142. The Kawamata-Viehweg vanishing theorem for schemes
Takumi Murayama
143. Minimal exponent and Hodge filtrations
Mircea Mustata
144. Inversion of adjunction for quotient singularities
Yusuke Nakamura
145. On compatifying moduli and degenerations of K-trivial varieties
Yuji Odaka
146. K-stability and birational superrigidity for Fano 3-fold weighted hypersurfaces
Takuzo Okada
147. Moduli space of semiorthogonal decompositions
Shinnosuke Okawa
148. Stable irrationality of the very general quartic fivefold
John Christian Ottem
149. Contact in algebraic and tropical geometry
Marco Pacini and Damiano Testa
150. Extended abstract of counting divisorial contractions with centre a cA_n-singularity
Erik Paemurru
151. Fine compactified Jacobians of nodal curves
Nicola Pagani
152. On polynomial automorphisms commuting with a simple derivation
Ivan Pan
153. K-moduli for log Fano complete intersections
Theodoros Stylianos Papazachariou
154. Cayley octads, plane quartic curves, Del Pezzo surfaces of degree 2, and double Veronese cones
Jihun Park
155. A Castelnuovo-Mumford regularity bound for threefolds with rational singularitie
Jinhyung Park
156. Moderately discontinuous algebraic topology and singularities
Maria Pe Pereira
157. Generic flexibility of cubic cones
Alexander Perepechko
158. Serre functors of semiorthogonal components
Alex Perry
159. Deformations of toric singularities and applications to K-moduli of Fano varieties
Andrea Petracci
160. Campana points on Fano varieties
Marta Pieropan
161. On canonical threefolds near the noether line
Roberto Pignatelli
162. K-stability and space sextic curves of genus three
Antoine Pinardin
163. On local-global principles and Galois cohomology
Alena Pirutka
164. Conic-line arrangements in the complex projective plane
Piotr Pokora
165. Hyperelliptic limits of quadrics through canonical curves and the super-Schottky locus
Alexander Polishchuk
166. General elephants for 3-fold extremal contractions
Yuri Prokhorov
167. Rationally connected rational double covers of primitive Fano varieties
Aleksandr Pukhlikov
168. Singularities and divisors in the moduli space of surfaces
Julie Rana
169. Sheaf counting of Hilbert schemes of points on C^4
Jorgen Rennemo
170. Wall-crossing pathologies in three dimensions
Fatemeh Rezaee
171. K-polystability of smooth Fano SL_2-threefolds
Jack Rogers
172. Hodge-Riemann classes and schur polynomials
Julius Ross
173. The splendour of asymptotically log Del Pezzos
Yanir Rubinstein
174. Smoothing toroidal crossing Fano 3-folds
Helge Ruddat
175. An overview on mordell-Weil rank jumps for fibers of elliptic surfaces
Cecilia Salgado
176. Blow-ups with log canonical singularities
Gregory Sankaran
177. On birational boundedness of some Calabi-Yau hypersurfaces
Taro Sano
178. Equivariant solidity of the three-dimensional projective space
Arman Sarikyan
179. Near-rationality properties of norm varieties
Anand Sawant
180. Generalized hyperpolygons and applications
Laura Schaposnik
181. Equality in the Bogomolov-Miyaoka-Yau inequality in the non-general type case
Stefan Schreieder
182. Rational curves on Enriques surfaces, but only few
Matthias Schuett
183. Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture
Junliang Shen
184. Survey of the article on Atiyah class and sheaf counting on local Calabi-Yau fourfolds
Artan Sheshmani
185. Automorphism groups of complex elliptic surfaces
Constantin Shramov
186. Lebrun-Salamon conjecture from the effective nonvanishing for Fano manifolds
Robert Smiech
187. Partial order on involutive permutations and double Schubert cells
Evgeny Smirnov
188. Geometric aspects of Kaehler-Einstein metrics on Klt pairs: a remark on optimal Bogomolov-Miyaoka-Yau inequality
Cristiano Spotti
189. Weak Del Pezzo surfaces with global vector fields
Claudia Stadlmayr
190. Local volumes of singularities and the mahler conjecture for convex bodies
Hendrik Suess
191. Higher order minimal families of rational curves on Fano manifolds
Taku Suzuki
192. An O-acyclic variety of even index
Fumiaki Suzuki
193. The Mukai model of M_7
David Swinarski
194. Local effectivity in projective spaces
Tomasz Szemberg
195. Fermat type arrangements and the containment problem
Justyna Szpond
196. Birational properties of base spaces of smooth projective families of good minimal models
Behrouz Taji
197. Key varieties for prime Q-Fano threefolds of codimension 4
Hiromichi Takagi
198. Deformations of F-pure and F-regular singularities
Shunsuke Takagi
199. On Mori fibre spaces in positive characteristic
Hiromu Tanaka
200. Rational curves on Fano threefolds
Sho Tanimoto
201. Delta invariants of quasi-smooth hypersurfaces
Luca Tasin
202. Real structures on almost homogeneous varieties
Ronan Terpereau
203. Mirror symmetry for fibrations and degenerations
Alan Thompson
204. On a logarithmic version of a theorem of Enriques
Sofia Tirabassi
205. Equivariant birational types
Yuri Tschinkel
206. Vector fields on canonically polarized surfaces
Nikos Tziolas
207. Noncommutative Del Pezzo surfaces
Kazushi Ueda
208. Exceptional collections on ?_2
Hokuto Uehara
209. Counts of secant planes to varieties, degenerations, and universal polynomials
Mara Ungureanu
210. Actions of Cremona groups on CAT(0) cube complexes
Christian Urech
211. Artin-Mumford counterexample, with generalizations, via Enriques surfaces
Alessandro Verra
212. Higher Fano manifolds
Nivedita Viswanathan
213. Global Brill-Noether theory over the Hurwitz space
Isabel Vogt
214. Positivity of the second exterior power of the tangent bundles
Kiwamu Watanabe
215. Pinched handle decompositions of finite simplicial complexes
Jean-Yves Welschinger
216. Concurrent exceptional curves on Del Pezzo surfaces of degree one and torsion points on elliptic fibrations
Rosa Winter
217. Rational maps via C^*-actions
Jaroslaw Wisniewski
218. On weighted Del Pezzo hypersurfaces
Joonyeong Won
219. Equivariant birational geometry of linear actions
Kaiqi Yang
220. Equivariant birational rigidity: around one question of Cheltsov and Kollar
Egor Yasinsky
221. Stringy motives and local fundamental groups of Klt surface singularities in arbitrary characteristic
Takehiko Yasuda
222. Degenerations, fibrations and mirror symmetry
Fenglong You
223. Stability of pencils of plane curves
Aline Zanardini
224. Jordan properties of automorphism groups of algebraic varieties and complex manifolds
Yuri Zarhin
225. Basis divisors and balanced metrics
Kewei Zhang
226. The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds
Zheng Zhang
227. Equivariant geometry of singular cubic threefolds
Zhijia Zhang
228. Topological SYZ fibrations with discriminant in codimension 2
Ilia Zharkov
229. Compact Kaehler threefolds with the action of an abelian group of maximal dynamical rank
Guolei Zhong
230. Equivariant K-stability under finite group action
Ziwen Zhu
231. K-stability of Fano varieties via admissible flags
Ziquan Zhuang
232. Unbounded connected algebraic subgroups of birational transformations
Sokratis Zikas
233. Finite quotients of Cremona groups
Susanna Zimmermann
