Determinantal Rings

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.

Autorentext
Udo Vetter ist Strafverteidiger mit Leib und Seele. Seit 2003 schreibt er das lawblog, das sich kritisch mit der Arbeit von Gerichten und Polizei auseinandersetzt. Die Seite zählt mit ca. 50 000 Besuchern täglich zu den meist gelesenen Blogs Deutschlands, wird häufig von Experten zitiert und wurde 2011 mit dem Grimme Online Award ausgezeichnet.

Inhalt
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 Kähler differentials.- Derivations and rigidity.