Commutative Algebra and its Interactions to Algebraic Geometry

VIASM 2013-2014
Springer (Verlag)
  • erschienen am 3. August 2018
  • Buch
  • |
  • Softcover
  • |
  • IX, 258 Seiten
978-3-319-75564-9 (ISBN)
This book presents four lectures on recent research in commutative algebra and its applications to algebraic geometry. Aimed at researchers and graduate students with an advanced background in algebra, these lectures were given during the Commutative Algebra program held at the Vietnam Institute of Advanced Study in Mathematics in the winter semester 2013 -2014. The first lecture is on Weyl algebras (certain rings of differential operators) and their D-modules, relating non-commutative and commutative algebra to algebraic geometry and analysis in a very appealing way. The second lecture concerns local systems, their homological origin, and applications to the classification of Artinian Gorenstein rings and the computation of their invariants. The third lecture is on the representation type of projective varieties and the classification of arithmetically Cohen -Macaulay bundles and Ulrich bundles. Related topics such as moduli spaces of sheaves, liaison theory, minimal resolutions, and Hilbert schemes of points are also covered. The last lecture addresses a classical problem: how many equations are needed to define an algebraic variety set-theoretically? It systematically covers (and improves) recent results for the case of toric varieties.
1st ed. 2018
  • Englisch
  • Cham
  • |
  • Schweiz
Springer International Publishing
  • Für Beruf und Forschung
  • 16 s/w Abbildungen, 1 farbige Abbildung
  • |
  • Bibliographie
  • Höhe: 234 mm
  • |
  • Breite: 156 mm
  • |
  • Dicke: 18 mm
  • 424 gr
978-3-319-75564-9 (9783319755649)
weitere Ausgaben werden ermittelt
1. Notes on Weyl Algebras and D-modules.- 2. Inverse Systems of Local Rings.- 3. Lectures on the Representation Type of a Projective Variety.- 4. Simplicial Toric Varieties which are set-theoretic Complete Intersections.
"The book is devoted to the life and work of Giovanni Battista Guccia ... . The book is highly recommended for historians of mathematics and historians of science at any stage of their career. The style also makes this book easy to read and the richness of the collected archival materials offers with extreme clarity an overview of the historical and cultural life of Sicily at the beginning of the 20th century." (Silvia De Bianchi, zbMATH 1400.01001, 2019)

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