论文标题
关于当地无自由商的引号方案的知识理论
On the Chow theory of Quot schemes of locally free quotients
论文作者
论文摘要
我们证明了$ quot $ schemes的食物组的公式，该公式在预期的尺寸条件下解决了向量束之间地图的变性基因座。该结果提供了一种统一的方式来理解各种几何形状情况的已知公式，例如爆炸，Cayley的窍门，Projectivization，Grassmannian Bundles，Springer型分辨率的拖鞋，以及提供新现象，例如用于Grassmannain类型flips/Flips/Flips/flops和虚拟拖鞋的公式。我们还为确定性理想，曲线线性序列的模量空间以及表面上的Hilbert方案提供了应用。
We prove a formula for Chow groups of $Quot$-schemes which resolve degeneracy loci of a map between vector bundles, under expected dimension conditions. This result provides a unified way to understand known formulae for various geometric situations such as blowups, Cayley's trick, projectivizations, Grassmannian bundles, flops from Springer type resolutions, as well as provide new phenomena such as formulae for Grassmannain type flips/flops and virtual flips. We also give applications to blowups of determinantal ideals, moduli spaces of linear series on curves, and Hilbert schemes of points on surfaces.
