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Determinants, Gröbner Bases and Cohomology

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...

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Bibliographic Details
Main Authors: Bruns, Winfried, Conca, Aldo (Author), Raicu, Claudiu (Author), Varbaro, Matteo (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2022, 2022
Edition:1st ed. 2022
Series:Springer Monographs in Mathematics
Subjects:
Commutative Algebra
Algebraic Geometry
Commutative Rings And Algebras
Algebra, Homological
Commutative Rings
Discrete Mathematics
Category Theory, Homological Algebra
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 1 Gröbner bases, initial ideals and initial algebras
  • 2 More on Gröbner deformations
  • 3 Determinantal ideals and the straightening law
  • 4 Gröbner bases of determinantal ideals
  • 5 Universal Gröbner bases
  • 6 Algebras defined by minors
  • 7 F-singularities of determinantal rings
  • 8 Castelnuovo–Mumford regularity
  • 9 Grassmannians, flag varieties, Schur functors and cohomology
  • 10 Asymptotic regularity for symbolic powers of determinantal ideals
  • 11 Cohomology and regularity in characteristic zero

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