Commutative Algebra and its Interactions to Algebraic Geometry VIASM 2013–2014

You must be logged in to access this title.

Sign up now

Already a member? Log in

Synopsis

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.

Book details

Series:
Lecture Notes in Mathematics (Book 2210)
Author:
Nguyen Tu Cuong, Le Tuan Hoa, Ngo Viet Trung
ISBN:
9783319755656
Related ISBNs:
9783319755649
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
Yes
Date of addition:
2018-10-17
Usage restrictions:
Copyright
Copyright date:
2018
Copyright by:
Springer International Publishing AG 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction