标题： K理论陈类公式用于棘手退化链 显示英文标题

标题： K-theoretic Chern class formulas for vexillary degeneracy loci

摘要： 使用提升算子和几何论证，我们建立了经典类型中退化位形的K-理论类的公式。 我们还发现了Giambelli所考虑的经典情况的新行列式和Pfaffian表达式：通用矩阵秩下降的位形，以及通用对称或反对称矩阵秩下降的位形。 在附录中，我们为具有二次型的偶数秩向量丛构造了一个K-理论欧拉类，改进了Edidin和Graham引入的Chow理论类。 我们还建立了最大迷向子丛的最高陈类之间的关系，这用于证明类型D的退化位形公式。 显示英文摘要

摘要： Using raising operators and geometric arguments, we establish formulas for the K-theory classes of degeneracy loci in classical types. We also find new determinantal and Pfaffian expressions for classical cases considered by Giambelli: the loci where a generic matrix drops rank, and where a generic symmetric or skew-symmetric matrix drops rank. In an appendix, we construct a K-theoretic Euler class for even-rank vector bundles with quadratic form, refining the Chow-theoretic class introduced by Edidin and Graham. We also establish a relation between top Chern classes of maximal isotropic subbundles, which is used in proving the type D degeneracy locus formulas.