Chern class formulas for quiver varieties
Chern class formulas for quiver varieties
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箭袋品种的陈省身公式
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
W. Fulton
中科院分区：
文献类型：
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作者：
A. Buch;W. Fulton
本文证明了与A_n型定向箭图有关的一般退化轨迹的一个公式.给定一个有限的矢丛序列，它们之间有映射，通过在这些映射的任意组合上施加秩条件来描述这些轨迹.我们的答案是所涉及的丛的Chern类中的多项式，这取决于给定的秩条件。它可以表示为舒尔多项式在丛的差中乘积的线性组合。这些系数是Littlewood-Richardson数的有趣推广。这些多项式专门给出了舒伯特多项式的新公式。
In this paper a formula is proved for the general degeneracy locus associated to an oriented quiver of type A_n. Given a finite sequence of vector bundles with maps between them, these loci are described by putting rank conditions on arbitrary composites of the maps. Our answer is a polynomial in Chern classes of the bundles involved, depending on the given rank conditions. It can be expressed as a linear combination of products of Schur polynomials in the differences of the bundles. The coefficients are interesting generalizations of Littlewood-Richardson numbers. These polynomials specialize to give new formulas for Schubert polynomials.