Determinantal Ideals
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Determinantal Ideals
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Author : Rosa M. Miró-Roig
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31
Determinantal Ideals written by Rosa M. Miró-Roig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.
This comprehensive overview of determinantal ideals includes an analysis of the latest results. Following the carefully structured presentation, you’ll develop new insights into addressing and solving open problems in liaison theory and Hilbert schemes. Three principal problems are addressed in the book: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; and unobstructedness and dimension of families of standard determinantal ideals. The author, Rosa M. Miro-Roig, is the winner of the 2007 Ferran Sunyer i Balaguer Prize.
Determinantal Ideals
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Author : Rosa M. Miro-Roig
language : en
Publisher:
Release Date : 2008
Determinantal Ideals written by Rosa M. Miro-Roig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Multiplier Ideals Of Determinantal Ideals
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Author : Amanda Ann Johnson
language : en
Publisher:
Release Date : 2003
Multiplier Ideals Of Determinantal Ideals written by Amanda Ann Johnson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Combinatorics Of Determinantal Ideals
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Author : Cornel Baetica
language : en
Publisher: Nova Publishers
Release Date : 2006
Combinatorics Of Determinantal Ideals written by Cornel Baetica and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Determinantal rings categories.
The study of determinantal ideals and of classical determinantal rings is an old topic of commutative algebra. As in most of the cases, the theory evolved from algebraic geometry, and soon became an important topic in commutative algebra. Looking back, one can say that it is the merit of Eagon and Northcott to be the first who brought to the attention of algebraists the determinantal ideals and investigated them by the methods of commutative and homological algebra. Later on, Buchsbaum and Eisenbud, in a long series of articles, went further along the way of homological investigation of determinantal ideals, while Eagon and Hochster studied them using methods of commutative algebra in order to prove that the classical determinantal rings are normal Cohen-Macaulay domains. As shown later by C. DeConcini, D. Eisenbud, and C. Procesi the appropriate framework including all three types of rings is that of algebras with straightening law, and the standard monomial theory on which these algebras are based yields computationally effective results. A coherent treatment of determinantal ideals from this point of view was given by Bruns and Vetter in their seminal book. The author's book aims to a thorough treatment of all three types of determinantal rings in the light of the achievements of the last fifteen years since the publication of Bruns and Vetter's book. They implicitly assume that the reader is familiar with the basics of commutative algebra. However, the authors include some of the main notions and results from Bruns and Vetter's book for the sake of completeness, but without proofs. The authors recommend the reader to first look at the book of Bruns and Vetter in order to get a feel for the flavour of this field. The author's book is meant to be a reference text for the current state of research in the theory of determinantal rings. It was structured in such a way that it can be used as textbook for a one semester graduate course in advanced topics in Algebra, and at the PhD level.
Determinantal Ideals Of Square Linear Matrices
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Author : Zaqueu Ramos
language : en
Publisher: Springer Nature
Release Date :
Determinantal Ideals Of Square Linear Matrices written by Zaqueu Ramos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Determinantal Ideals
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Author : Cornel Băeţica
language : en
Publisher:
Release Date : 2003
Determinantal Ideals written by Cornel Băeţica and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
On Determinantal Ideals Which Are Set Theoretic Complete Intersections
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Author : Giuseppe Valla
language : en
Publisher:
Release Date : 1980
On Determinantal Ideals Which Are Set Theoretic Complete Intersections written by Giuseppe Valla and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
Determinants Gr Bner Bases And Cohomology
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Author : Winfried Bruns
language : en
Publisher: Springer Nature
Release Date : 2022-12-02
Determinants Gr Bner Bases And Cohomology written by Winfried Bruns and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-02 with Mathematics categories.
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 interesting and important class of varieties.
Determinantal Rings
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Author : Winfried Bruns
language : en
Publisher: Springer
Release Date : 2006-11-14
Determinantal Rings written by Winfried Bruns and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.
Products Of Generalized Determinantal Ideals And Decompositions Under The Action Of General Linear Groups
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Author : Karen Louise Whitehead
language : en
Publisher:
Release Date : 1982
Products Of Generalized Determinantal Ideals And Decompositions Under The Action Of General Linear Groups written by Karen Louise Whitehead and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.