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Determinants, Gröbner Bases and Cohomology by Winfried Bruns, Aldo Conca, Claudiu Raicu, Matteo Varbaro is a nonfiction available to read on EtoBox.

What is Determinants, Gröbner Bases and Cohomology about?

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 prese

Who reads Determinants, Gröbner Bases and Cohomology?

Author

Winfried Bruns, Aldo Conca, Claudiu Raicu, Matteo Varbaro

Publisher

Springer International Publishing Springer

Published

2022

Language

EN

ISBN

9783031054792

Category

nonfiction

Subjects

Mathematics, Algebra, Stem