Author | Fulton, William. author |
---|---|

Title | Schubert Varieties and Degeneracy Loci [electronic resource] / by William Fulton, Piotr Pragacz |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1998 |

Connect to | http://dx.doi.org/10.1007/BFb0096380 |

Descript | X, 150 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Algebraic geometry
Group theory
Algebraic topology
Combinatorics
Mathematics
Algebraic Geometry
Combinatorics
Group Theory and Generalizations
Algebraic Topology