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, 00758434 ; 2210


Lecture notes in mathematics, ; 2210

附註 
1. Notes on Weyl Algebras and Dmodules  2. Inverse Systems of Local Rings  3. Lectures on the Representation Type of a Projective Variety  4. Simplicial Toric Varieties which are settheoretic 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 Dmodules, relating noncommutative 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 settheoretically? 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)

