What Determines an Algebraic Variety?

Name: What Determines an Algebraic Variety? | (AMS-216)
Brand: Princeton University Press
Price: 73.49 EUR
Availability: OnlineOnly

(AMS-216)

János Kollár Max Lieblich Martin Olsson Will Sawin(Autor*in)

Princeton University Press

1. Auflage

Erschienen am 25. Juli 2023

240 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-0-691-24683-3 (ISBN)

73,49 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Personen

Inhalt

Cover
Contents
Preface
Acknowledgments
1. Introduction
1.1 From lines and planes to the Zariski topology of Pn
1.2 The main theorem
1.3 Organization of the book
2. Preliminaries
2.1 Algebraic varieties
2.2 Examples and speculations
2.3 Scheme-theoretic formulation
2.4 Survey of related results
2.5 Terminology and notation
3. The fundamental theorem of projective geometry
3.1 The fundamental theorem of definable projective geometry
3.2 A variant fundamental theorem
3.3 The probabilistic fundamental theorem of projective geometry
4. Divisorial structures and definable linear systems
4.1 Divisorial structures
4.2 Remarks on divisors
4.3 Definable subspaces in linear systems
5. Reconstruction from divisorial structures: infinite fields
5.1 Reduction to the quasi-projective case
5.2 The quasi-projective case
5.3 Counterexamples in dimension 1
6. Reconstruction from divisorial structures: finite fields
6.1 The Bertini-Poonen theorem
6.2 Preparatory lemmas
6.3 Reconstruction over finite fields
7. Topological geometry
7.1 Pencils
7.2 Fibers of finite morphisms
7.3 Topological pencils
7.4 Degree functions and algebraic pencils
7.5 Degree functions and linear equivalence
7.6 Uncountable fields
8. The set-theoretic complete intersection property
8.1 Summary of results
8.2 Set-theoretic complete intersection property
8.3 Mordell-Weil fields
8.4 Reducible scip subsets
8.5 Projective spaces
8.6 Appendix: Special fields
9. Linkage
9.1 Linkage of divisors
9.2 Preparations: Sections and their zero sets
9.3 Néron's theorem and consequences
9.4 Linear similarity
9.5 Bertini-Hilbert dimension
9.6 Linkage of divisors and residue fields
9.7 Minimally restrictive linking and transversality
9.8 Recovering linear equivalence
9.9 Appendix: Weakly Hilbertian fields
10. Complements, counterexamples, and conjectures
10.1 A topological Gabriel theorem
10.2 Examples over finite fields
10.3 Surfaces over locally finite fields
10.4 Real Zariski topology
10.5 Countable noetherian topologies
10.6 Conjectures
11. Appendix
11.1 Bertini-type theorems
11.2 Complete intersections
11.3 Picard group, class group, and Albanese variety
Bibliography
Index of Notation
Index of Terminology

Systemvoraussetzungen

Als PDF speichern Als Link merken