投影曲面的Vafa-Witten不变量I:稳定情形

IF 0.9 1区 数学 Q2 MATHEMATICS
Yuuji Tanaka, Richard P. Thomas
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引用次数: 68

摘要

在极化表面上,瓦法·维滕方程的解对应于某些多稳态希格斯对。当稳定性和半稳定性一致时,模空间允许对称阻塞理论和具有紧固定轨迹的C*\mathbb{C}^*作用。应用虚拟局部化,我们定义了变形下的不变量常数。当Vafa Witten的消失定理成立时,结果是瞬时模空间的(有符号)Euler特征。总的来说,还有其他合理的贡献。这些在具有正正则丛的曲面上的计算恢复了Vafa和Witten预测的模形式的第一项。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Vafa-Witten invariants for projective surfaces I: stable case
On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a C ∗ \mathbb {C}^* action with compact fixed locus. Applying virtual localisation we define invariants constant under deformations. When the vanishing theorem of Vafa-Witten holds, the result is the (signed) Euler characteristic of the moduli space of instantons. In general there are other, rational, contributions. Calculations of these on surfaces with positive canonical bundle recover the first terms of modular forms predicted by Vafa and Witten.
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来源期刊
CiteScore
2.70
自引率
5.60%
发文量
23
审稿时长
>12 weeks
期刊介绍: The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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