Commutative algebra and its interactions
β Cuong N.T (ed.)
π Library
π
2018
π Springer
π English
β¦ LIBER β¦
π
Commutative Algebra and its Interactions to Algebraic Geometry
β Scribed by Nguyen Tu CUONG, Le Tuan HOA, Ngo Viet TRUNG
- Publisher
- Springer International Publishing
- Year
- 2018
- Tongue
- English
- Leaves
- 265
- Series
- Lecture Notes in Mathematics 2210
- Edition
- 1st ed.
- Category
- Library
β¬ Acquire This Volume
No coin nor oath required. For personal study only.
β¦ 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.
β¦ Table of Contents
Front Matter ....Pages i-ix
Notes on Weyl Algebra and D-Modules (Markus Brodmann)....Pages 1-117
Inverse Systems of Local Rings (Juan Elias)....Pages 119-163
Lectures on the Representation Type of a Projective Variety (Rosa M. MirΓ³-Roig)....Pages 165-216
Simplicial Toric Varieties Which Are Set-Theoretic Complete Intersections (Marcel Morales)....Pages 217-256
Back Matter ....Pages 257-258
β¦ Subjects
Mathematics; Commutative Rings and Algebras; Algebraic Geometry; Associative Rings and Algebras; Partial Differential Equations
π SIMILAR VOLUMES
Commutative Algebra: Interactions with A
β Avramov L.L., et al. (eds.)
π Library
π
2003
π AMS
π English
Algebraic Geometry and Commutative Algeb
β Siegfried Bosch
π Library
π
2012
π Springer
π English
Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieckβs schemes invented in the late 1950s allowed the application of algeb
Algebraic geometry and commutative algeb
β S Bosch
π Library
π
2013
π Springer
π English
Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck's schemes invented in the late 1950s allowed the application of alge
Algebraic Geometry and Commutative Algeb
β Siegfried Bosch (auth.)
π Library
π
2013
π Springer-Verlag London
π English
<p><p>Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieckβs schemes invented in the late 1950s allowed the application of
Algebraic Geometry and Commutative Algeb
β Siegfried Bosch
π Library
π
2022
π Springer-Verlag London Ltd
π English
Algebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry. It transcends the limited scope of pure Algebra by means of geometric construction principles. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s b