Commutative Algebra and its Interactions to Algebraic Geometry

VIASM 2013–2014

Nguyen Tu CUONG, Le Tuan HOA, Ngo Viet TRUNG (Herausgeber)

Buch | Softcover

IX, 258 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-75564-9 (ISBN)

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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.

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.

"The book is devoted to the life and work of Giovanni Battista Guccia ... . The book is highly recommended for historians of mathematics and historians of science at any stage of their career. The style also makes this book easy to read and the richness of the collected archival materials offers with extreme clarity an overview of the historical and cultural life of Sicily at the beginning of the 20th century." (Silvia De Bianchi, zbMATH 1400.01001, 2019)

Erscheinungsdatum	04.08.2018
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	IX, 258 p. 17 illus., 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	412 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Arithmetically Cohen-Macaulay Bundle • Artinian Gorenstein Ring • D-Module • Local System • Partial differential equations • Representation Type • Set-theoretically Complete Intersection • Toric Varieties • Weyl algebra
ISBN-10	3-319-75564-1 / 3319755641
ISBN-13	978-3-319-75564-9 / 9783319755649
Zustand	Neuware