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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Determinants, Gröbner Bases and Cohomology
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Determinants, Gröbner Bases and Cohomology
Winfried Bruns, Aldo Conca, Claudiu Raicu, Matteo Varbaro (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
03.12.2023
Sprache
Englisch
EAN
9783031054822
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Winfried Bruns, Aldo Conca, Claudiu Raicu, Matteo Varbaro
Seitenanzahl
507
Einbandart
Broschiert
Schlagwörter
Determinantal varieties, Determinantal ideals, Determinantal rings, Sagbi bases, initial ideals, initial algebras, Robinson-Schensted-Knuth correspondence, straightening law, F-regularity, Castelnuovo-Mumford regularity, cohomology of flag varieties, line bundles on flag varieties, Schur functors, Borel-Weil-Bott theorem, regularity of symbolic powers
Thema-Inhalt
PBMW - Algebraische Geometrie
PBF - Algebra
PBD - Diskrete Mathematik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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