Editors:
- Suitable for graduate courses, requiring only a basic background in commutative algebra
- Includes many interesting open problems and ideas for further investigation
- Describes recent research in commutative algebra and its applications to algebraic geometry
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2210)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
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.
Editors and Affiliations
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Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
Nguyen Tu CUONG, Le Tuan HOA, Ngo Viet TRUNG
Bibliographic Information
Book Title: Commutative Algebra and its Interactions to Algebraic Geometry
Book Subtitle: VIASM 2013–2014
Editors: Nguyen Tu CUONG, Le Tuan HOA, Ngo Viet TRUNG
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-75565-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-75564-9Published: 03 August 2018
eBook ISBN: 978-3-319-75565-6Published: 02 August 2018
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 258
Number of Illustrations: 16 b/w illustrations, 1 illustrations in colour
Topics: Commutative Rings and Algebras, Algebraic Geometry, Associative Rings and Algebras, Partial Differential Equations