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書名 Commutative algebra and its interactions to algebraic geometry : VIASM 2013-2014 / edited by Nguyen Tu CUONG, Le Tuan HOA, Ngo Viet TRUNG
出版項 Cham : Springer International Publishing : Imprint: Springer, 2018
國際標準書號 9783319755656 (electronic bk.)
9783319755649 (paper)
國際標準號碼 10.1007/978-3-319-75565-6 doi
book jacket
說明 1 online resource (ix, 258 pages) : illustrations, digital ; 24 cm
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
系列 Lecture notes in mathematics, 0075-8434 ; 2210
Lecture notes in mathematics, ; 2210
附註 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
Host Item Springer eBooks
主題 Mathematics
Geometry, Algebraic
Associative rings
Rings (Algebra)
Commutative algebra
Commutative rings
Differential equations,
Mathematics
Commutative Rings and Algebras
Algebraic Geometry
Associative Rings and Algebras
Partial Differential Equations
Alt Author Tu cuong, nguyen, editor
Tuan Hoa, Le, editor
Viet Trung, Ngo, editor
SpringerLink (Online service)
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