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Virtual χ−y-genera of Quot schemes on surfaces
Journal of the London Mathematical Society ( IF 1.0 ) Pub Date : 2021-04-15 , DOI: 10.1112/jlms.12460 Woonam Lim 1
Journal of the London Mathematical Society ( IF 1.0 ) Pub Date : 2021-04-15 , DOI: 10.1112/jlms.12460 Woonam Lim 1
Affiliation
This paper studies the virtual -genera of Grothendieck's Quot schemes on surfaces, thus refining the calculations of the virtual Euler characteristics by Oprea–Pandharipande. We first prove a structural result expressing the equivariant virtual -genera of Quot schemes universally in terms of the Seiberg–Witten invariants. The formula is simpler for curve classes of Seiberg–Witten length , which are defined in the paper. By way of application, we give complete answers in the following cases:
中文翻译:
表面上 Quot 方案的虚拟 χ−y 属
本文研究了虚拟 -格洛腾迪克在表面上的报价方案的属,从而改进了 Oprea-Pandharipande 对虚拟欧拉特征的计算。我们首先证明了表达等变虚拟的结构结果- 根据 Seiberg-Witten 不变量,Quot 方案的种类普遍存在。对于 Seiberg-Witten 长度的曲线类,公式更简单,在论文中定义。通过应用,我们在以下情况下给出完整的答案:
更新日期:2021-04-15
- (i) arbitrary surfaces for the zero curve class;
- (ii) relatively minimal elliptic surfaces for rational multiples of the fiber class;
- (iii) minimal surfaces of general type with for any curve classes.
中文翻译:
表面上 Quot 方案的虚拟 χ−y 属
本文研究了虚拟 -格洛腾迪克在表面上的报价方案的属,从而改进了 Oprea-Pandharipande 对虚拟欧拉特征的计算。我们首先证明了表达等变虚拟的结构结果- 根据 Seiberg-Witten 不变量,Quot 方案的种类普遍存在。对于 Seiberg-Witten 长度的曲线类,公式更简单,在论文中定义。通过应用,我们在以下情况下给出完整的答案:
- (i)零曲线类的任意曲面;
- (ii)纤维类有理倍数的相对最小的椭圆表面;
- (iii)具有一般类型的最小表面 对于任何曲线类。