Bruns Determinants, Gr?bner Bases and Cohomology 9783031054792

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Автор: Bruns
Название: Determinants, Gr?bner Bases and Cohomology
ISBN: 9783031054792
Издательство: Springer
Классификация:

Дискретная математика

Алгебра

Алгебраическая геометрия

ISBN-10: 3031054792
Обложка/Формат: Hardback
Страницы: 507
Вес: 0.95 кг.
Дата издания: 17.12.2022
Серия: Springer Monographs in Mathematics
Язык: English
Издание: 1st ed. 2022
Иллюстрации: 21 illustrations, black and white; xiii, 507 p. 21 illus.; 21 illustrations, black and white; xiii, 507 p. 21 illus.
Размер: 235 x 155
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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 Gr?bner 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 Gr?bner 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, Gr?bner 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 interesting and important class of varieties.
Дополнительное описание: 1 Gr?bner bases, initial ideals and initial algebras.- 2 More on Gr?bner deformations.- 3 Determinantal ideals and the straightening law.- 4 Gr?bner bases of determinantal ideals.- 5 Universal Gr?bner bases.- 6 Algebras defined by minors.- 7 F-singulariti

Determinants, Gr?bner Bases and Cohomology, Bruns