Schubert complexes and degeneracy loci

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• 作者：Steven V Sam^a ; ^{ssam@math.mit.edu"" rel=""nofollow} ;
• 关键词：Complexes ; Degeneracy loci ; Schubert varieties ; Cohomology classes ; Schubert polynomials ; Polynomial functors
• 刊名：Journal of Algebra
• 出版年：2011
• 出版时间：1 July 2011
• 年：2011
• 卷：337
• 期：1
• 页码：103-125
• 全文大小：356 K

文摘

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 Kraśkiewicz 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.