单极子对改进的vfa - witteninvariants的贡献

IF 2 1区数学

Geometry & Topology Pub Date : 2018-09-30 DOI:10.2140/gt.2020.24.2781

T. Laarakker

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引用次数: 24

摘要

我们研究了单极子对最近由Maulik和Thomas定义的精炼Vafa-Witten不变量的贡献[13]。我们应用Gholampour和Thomas[7]的结果证明了一维权空间中希格斯对的贡献序列生成的一个普惠性结果。对于素数秩，根据托马斯定理，这些解释了整个单极子的贡献。我们使用环向计算来确定部分生成序列，并发现与G\ \ ottsche和Kool[10]对秩2和秩3的猜想一致。

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Monopole contributions to refined Vafa–Witten invariants

We study the monopole contribution to the refined Vafa-Witten invariant, recently defined by Maulik and Thomas [13]. We apply results of Gholampour and Thomas [7] to prove a universality result for the generating series of contributions of Higgs pairs with 1-dimensional weight spaces. For prime rank, these account for the entire monopole contribution, by a theorem of Thomas. We use toric computations to determine part of the generating series, and find agreement with the conjectures of G\"ottsche and Kool [10] for rank 2 and 3.

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来源期刊

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.