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Author: Rosa M. Miró-Roig
Publisher: Springer Science & Business Media
ISBN: 3764385359
Category : Mathematics
Languages : en
Pages : 149
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Book Description
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.
Author: Rosa M. Miró-Roig
Publisher: Springer Science & Business Media
ISBN: 3764385359
Category : Mathematics
Languages : en
Pages : 149
Get Book Here
Book Description
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.
Author: Cornel Baetica
Publisher: Nova Publishers
ISBN: 9781594549182
Category : Determinantal rings
Languages : en
Pages : 156
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Book Description
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.
Author: Zaqueu Ramos
Publisher: Springer Nature
ISBN: 3031552849
Category :
Languages : en
Pages : 326
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Book Description
Author: Amanda Ann Johnson
Publisher:
ISBN:
Category :
Languages : en
Pages : 196
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Book Description
Author: Jürgen Herzog
Publisher: Springer Science & Business Media
ISBN: 9400710925
Category : Mathematics
Languages : en
Pages : 277
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Book Description
Proceedings of the NATO Advanced Research Workshop, held in Sinaia, Romania, 17-22 September 2002
Author: Karen Louise Whitehead
Publisher:
ISBN:
Category :
Languages : en
Pages : 216
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Book Description
Author: Winfried Bruns
Publisher: Springer
ISBN: 3540392742
Category : Mathematics
Languages : en
Pages : 246
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Book Description
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.
Author: Kevin Buzzard
Publisher: Springer Nature
ISBN: 3031645294
Category :
Languages : en
Pages : 377
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Book Description
Author: Ezra Miller
Publisher: Springer Science & Business Media
ISBN: 9780387237077
Category : Mathematics
Languages : en
Pages : 442
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Book Description
Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs
Author: Hideyuki Matsumura
Publisher: Cambridge University Press
ISBN: 9780521367646
Category : Mathematics
Languages : en
Pages : 338
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Book Description
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
