Determinantal rings
Author(s)
Bibliographic Information
Determinantal rings
（Lecture notes in mathematics, 1327 . Instituto de Matemática Pura e Aplicada,
Springer-Verlag, c1988
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Available at / 76 libraries
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Library & Science Information Center, Osaka Prefecture University
: usNDC6:410.8||L||132710091531611
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||13278808028S
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: gwDC19:510/L4972070092605
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Note
Bibliography: p. [219]-228
Includes indexes
Description and Table of Contents
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.
Table of Contents
Preliminaries.- Ideals of maximal minors.- Generically perfect ideals.- Algebras with straightening law on posets of minors.- The structure of an ASL.- Integrity and normality. The singular locus.- Generic points and invariant theory.- The divisor class group and the canonical class.- Powers of ideals of maximal minors.- Primary decomposition.- Representation theory.- Principal radical systems.- Generic modules.- The module of Kahler differentials.- Derivations and rigidity.
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