Schubert complexes and degeneracy loci

JOURNAL OF ALGEBRA

卷:337

Article

Sam, Steven V.

关键词: Complexes;    Degeneracy loci;    Schubert varieties;    Cohomology classes;    Schubert polynomials;    Polynomial functors;   

DOI  :  10.1016/j.jalgebra.2011.04.032

来源: Elsevier

【 摘 要 】

Given a generic map between flagged vector bundles on a Cohen-Macaulay variety, we construct maximal Cohen-Macaulay modules with linear resolutions supported on the Schubert-type degeneracy loci. The linear resolution is provided by the Schubert complex, which is the main tool introduced and studied in this paper. These complexes extend the Schubert functors of Kraskiewicz and Pragacz, and were motivated by the fact that Schur complexes resolve maximal Cohen-Macaulay modules supported on determinantal varieties. The resulting formula in K-theory provides a linear approximation of the structure sheaf of the degeneracy locus, which can be used to recover a formula due to Fulton. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free