箭簇品种的陈类公式
代数几何
2009-10-31 v1
摘要
本文证明了一个关于 A_n 型有向箭簇的一般退化 locus 的公式。给定一串向量丛及其间的映射，这些 locus 通过对映射的任意复合施加秩条件来描述。我们的答案是所涉及丛的陈类的一个多项式，依赖于给定的秩条件。它可以表示为这些丛的差值中 Schur 多项式乘积的线性组合。系数是 Littlewood-Richardson 数的有趣推广。这些多项式可特化给出 Schubert 多项式的新公式。
引用
@article{arxiv.math/9804041,
title = {Chern class formulas for quiver varieties},
author = {Anders S. Buch and William Fulton},
journal= {arXiv preprint arXiv:math/9804041},
year = {2009}
}
备注
17 pages, 20 figures. The document is available as a .tar.gz file containing one LaTeX2e file and 20 (included) postscript files. Packages xypic and psfrag are used. Note that when viewed with xdvi, the text in figures looks bad, but it comes out right when printed. The paper is also available as one postscript file at http://www.math.uchicago.edu/~abuch/papers/quiver.ps.gz