Synopses & Reviews
The central theme of this book is a detailed exposition of the geometric technique of calculating syzygies. While this is an important tool in algebraic geometry, Jerzy Weyman has elected to write from the point of view of commutative algebra in order to avoid being tied to special cases from geometry. No prior knowledge of representation theory is assumed. Chapters on several applications are included, and numerous exercises will give the reader insight into how to apply this important method.
Includes bibliographical references (p. 359-366) and indexes.
The central theme of this book is an exposition of the geometric technique of calculating syzygies. Written from a point of view of commutative algebra, no knowledge of representation theory is assumed. Several important applications are carefully considered, with numerous exercises for the reader.
An exposition of the important geometric technique of calculating syzygies.
Table of Contents
1. Introduction; 2. Schur functions and Schur complexes; 3. Grassmannians and flag varieties; 4. Bott's theorem; 5. The geometric technique; 6. The determinantal varieties; 7. Higher rank varieties; 8. The nilpotent orbit closures; 9. Resultants and discriminants.