Overview
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.
Full Product Details
Author: Nguyen Tu CUONG ,
Le Tuan HOA ,
Ngo Viet TRUNG
Publisher: Springer International Publishing AG
Imprint: Springer International Publishing AG
Edition: 1st ed. 2018
Volume: 2210
Weight: 0.454kg
ISBN: 9783319755649
ISBN 10: 3319755641
Pages: 258
Publication Date: 03 August 2018
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
""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)
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)
"""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)"
