Téléchargez le livre : Determinants, Gröbner Bases and Cohomology

Determinants, Gröbner Bases and Cohomology

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Springer


Paru le : 2022-12-02

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Description

This book offers an up-to-date, comprehensive account of determinantal rings and varieties, presenting a multitude of methods used in their study, with tools from combinatorics, algebra, representation theory and geometry.


After a concise introduction to Gröbner and Sagbi bases, determinantal ideals are studied via the standard monomial theory and the straightening law. This opens the door for representation theoretic methods, such as the Robinson–Schensted–Knuth correspondence, which provide a description of the Gröbner bases of determinantal ideals, yielding homological and enumerative theorems on determinantal rings. Sagbi bases then lead to the introduction of toric methods. In positive characteristic, the Frobenius functor is used to study properties of singularities, such as F-regularity and F-rationality. Castelnuovo–Mumford regularity, an important complexity measure in commutative algebra and algebraic geometry, is introduced in the general setting of a Noetherian base ring and then applied to powers and products of ideals. The remainder of the book focuses on algebraic geometry, where general vanishing results for the cohomology of line bundles on flag varieties are presented and used to obtain asymptotic values of the regularity of symbolic powers of determinantal ideals. In characteristic zero, the Borel–Weil–Bott theorem provides sharper results for GL-invariant ideals. The book concludes with a computation of cohomology with support in determinantal ideals and a survey of their free resolutions.


Determinants, Gröbner Bases and Cohomology provides a unique reference for the theory of determinantal ideals and varieties, as well as an introduction to the beautiful mathematics developed in their study. Accessible to graduate students with basic grounding in commutative algebra and algebraic geometry, it can be used alongside general texts to illustrate the theory with a particularly interestingand important class of varieties.
Pages
507 pages
Collection
n.c
Parution
2022-12-02
Marque
Springer
EAN papier
9783031054792
EAN PDF
9783031054808
Informations sur l'ebook
Nombre pages copiables
5
Nombre pages imprimables
50
Taille du fichier
6410 Ko
Prix
147,69 €
EAN EPUB
9783031054808
Informations sur l'ebook
Nombre pages copiables
5
Nombre pages imprimables
50
Taille du fichier
45158 Ko
Prix
147,69 €

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