Fulton, William.
Schubert Varieties and Degeneracy Loci [electronic resource] / by William Fulton, Piotr Pragacz. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1998. - X, 150 p. online resource. - Lecture Notes in Mathematics, 1689 0075-8434 ; . - Lecture Notes in Mathematics, 1689 .
to degeneracy loci and schubert polynomials -- Modern formulation; Grassmannians, flag varieties, schubert varieties -- Symmetric polynomials useful in geometry -- Polynomials supported on degeneracy loci -- The Euler characteristic of degeneracy loci -- Flag bundles and determinantal formulas for the other classical groups -- and polynomial formulas for other classical groups -- The classes of Brill-Noether loci in Prym varieties -- Applications and open problems.
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.
9783540698043
10.1007/BFb0096380 doi
Mathematics.
Geometry, algebraic.
Group theory.
Combinatorics.
Algebraic topology.
Mathematics.
Algebraic Geometry.
Combinatorics.
Group Theory and Generalizations.
Algebraic Topology.
QA564-609
516.35
Schubert Varieties and Degeneracy Loci [electronic resource] / by William Fulton, Piotr Pragacz. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1998. - X, 150 p. online resource. - Lecture Notes in Mathematics, 1689 0075-8434 ; . - Lecture Notes in Mathematics, 1689 .
to degeneracy loci and schubert polynomials -- Modern formulation; Grassmannians, flag varieties, schubert varieties -- Symmetric polynomials useful in geometry -- Polynomials supported on degeneracy loci -- The Euler characteristic of degeneracy loci -- Flag bundles and determinantal formulas for the other classical groups -- and polynomial formulas for other classical groups -- The classes of Brill-Noether loci in Prym varieties -- Applications and open problems.
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.
9783540698043
10.1007/BFb0096380 doi
Mathematics.
Geometry, algebraic.
Group theory.
Combinatorics.
Algebraic topology.
Mathematics.
Algebraic Geometry.
Combinatorics.
Group Theory and Generalizations.
Algebraic Topology.
QA564-609
516.35