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3 produkter
3 produkter
Del 2210 - Lecture Notes in Mathematics
Commutative Algebra and its Interactions to Algebraic Geometry
VIASM 2013–2014
Häftad, Engelska, 2018
760 kr
Skickas inom 10-15 vardagar
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.
950 kr
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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.
Inbunden, Engelska, 1994
1 669 kr
Skickas inom 3-6 vardagar
In a relatively short time, commutative algebra has grown in many directions. Over a period of nearly fifty years starting from the so-called homological period till today, the area has developed into a rich laboratory of methods, structures and problem-solving tools.One could say a distinct modern trend of commutative algebra is a strong interaction with various aspects of Combinatorics and Computer Algebra. This has resulted in a new sense of measuring for old assumptions, and a better understanding of old results.At the same time, Invariant Theory and Algebraic Geometry remain constituents of an everlasting classical source, responsible for important themes that have been developed in Commutative Algebra — such as deformation, linkage, algebraic tori and determinantal rings, etc.This volume of proceedings is well-entrenched on the lines of development outlined above. As such, it aims to keep researchers and mathematicians well-informed of the developments in the field.