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Degeneracy loci, virtual cycles and nested Hilbert schemes II
Compositio Mathematica ( IF 1.3 ) Pub Date : 2020-08-01 , DOI: 10.1112/s0010437x20007290
Amin Gholampour , Richard P. Thomas

We express nested Hilbert schemes of points and curves on a smooth projective surface as ‘virtual resolutions’ of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories to produce the virtual cycles of Vafa–Witten theory and other sheaf-counting problems. The result is an effective way of calculating invariants (VW, SW, local PT and local DT) via Thom–Porteous-like Chern class formulae.

中文翻译:

简并位点、虚拟循环和嵌套希尔伯特方案 II

我们将平滑投影面上的点和曲线的嵌套希尔伯特方案表示为平滑环境空间上向量束映射的简并轨迹的“虚拟分辨率”。我们展示了如何修改由此产生的阻塞理论以产生 Vafa-Witten 理论和其他捆计数问题的虚拟循环。结果是通过类 Thom-Porteous 陈类公式计算不变量(VW、SW、局部 PT 和局部 DT)的有效方法。
更新日期:2020-08-01
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