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＜電子ブック＞
Commutative Algebra and its Interactions to Algebraic Geometry : VIASM 2013–2014 / edited by Nguyen Tu CUONG, Le Tuan HOA, Ngo Viet TRUNG
(Lecture Notes in Mathematics. ISSN:16179692 ; 2210)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	IX, 258 p. 17 illus., 1 illus. in color : online resource
著者標目	Tu CUONG, Nguyen editor Tuan HOA, Le editor Viet TRUNG, Ngo editor SpringerLink (Online service)
件　名	LCSH:Commutative algebra LCSH:Commutative rings LCSH:Algebraic geometry LCSH:Associative rings LCSH:Associative algebras LCSH:Differential equations FREE:Commutative Rings and Algebras FREE:Algebraic Geometry FREE:Associative Rings and Algebras FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-75565-6

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