Schubert Varieties and Degeneracy Loci

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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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.

• Algebraic geometry
• Combinatorics
• Euler characteristic
• algebra
• algebraic groups
• algebraic topology

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