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Schubert Varieties and Degeneracy Loci

  • Book
  • © 1998

Overview

Authors:
  1. William Fulton
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  2. Piotr Pragacz
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1689)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction to degeneracy loci and schubert polynomials

    • William Fulton, Piotr Pragacz
    Pages 1-13

  3. Modern formulation; Grassmannians, flag varieties, schubert varieties

    • William Fulton, Piotr Pragacz
    Pages 14-25

  4. Symmetric polynomials useful in geometry

    • William Fulton, Piotr Pragacz
    Pages 26-39

  5. Polynomials supported on degeneracy loci

    • William Fulton, Piotr Pragacz
    Pages 40-52

  6. The Euler characteristic of degeneracy loci

    • William Fulton, Piotr Pragacz
    Pages 53-64

  7. Flag bundles and determinantal formulas for the other classical groups

    • William Fulton, Piotr Pragacz
    Pages 65-78

  8. and polynomial formulas for other classical groups

    • William Fulton, Piotr Pragacz
    Pages 79-91

  9. The classes of Brill-Noether loci in Prym varieties

    • William Fulton, Piotr Pragacz
    Pages 92-96

  10. Applications and open problems

    • William Fulton, Piotr Pragacz
    Pages 97-103

  11. Back Matter

    Pages 104-148
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Keywords

About this book

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and algebraic geometry.

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