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Monopole contributions to
refined Vafa–Witten invariants
Ties Laarakker |
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Geometry & Topology 24 (2020) 2781–2828
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DOI: 10.2140/gt.2020.24.2781
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Abstract |
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We study the monopole contribution to the refined Vafa–Witten invariant recently defined by Maulik and Thomas (work in progress). We apply the results of Gholampour and Thomas (to appear in Compos. Math.) to prove a universality result for the generating series of contributions of Higgs pairs with –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 Göttsche and Kool (Pure Appl. Math. Q. 14 (2018) 467–513) for ranks and . |
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Keywords
Vafa–Witten invariants, monopole contribution, VW
invariants
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Mathematical Subject Classification 2010
Primary: 14C05, 14D20, 14J80
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References |
Publication
Received: 10 February 2019
Revised: 8 July 2019
Accepted: 9 December 2019
Published: 29 December 2020
Proposed: Lothar Göttsche
Seconded: Jim Bryan, Paul Seidel
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Authors |
| Ties Laarakker | |
| Imperial College London United Kingdom |
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