Lecture Notes in Mathematics

By: William Fulton, Piotr Pragacz

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Paperback | 16 July 1998

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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.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Geometry Algebraic Geometry Groups & Group Theory Combinatorics & Graph Theory Algebra Topology Algebraic Topology

Preface
Introduction to degeneracy loci and Schubert polynomials	p. 1
Modern formulation: Grassmannians, flag varieties, Schubert varieties	p. 14
Symmetric polynomials useful in geometry	p. 26
Polynomials supported on degeneracy loci	p. 40
The Euler characteristic of degeneracy loci	p. 53
Flag manifolds and determinantal formulas for other classical groups	p. 65
P- and Q-polynomial formulas for other classical groups	p. 79
The classes of Brill-Noether loci in Prym varieties	p. 92
Applications and open problems	p. 97
Intersection theory; polynomials representing degeneracy loci	p. 104
Vexillary permutations and multi-Schur polynomials	p. 109
Bott-Samelson schemes	p. 112
Pfaffians	p. 115
Group-theoretic approaches	p. 118
Push-forward formulas	p. 124
The classes of relative diagonals	p. 127
A construction of Mumford	p. 129
Schur-Weyl modules	p. 131
Quantum double Schubert polynomials	p. 134
Bibliography	p. 139
Index of Notation	p. 143
General Index	p. 146
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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