Monopole contributions to refined Vafa–Witten invariants

Laarakker, Ties

doi:10.2140/gt.2020.24.2781

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Monopole contributions to refined Vafa–Witten invariants

Ties Laarakker

Geometry & Topology 24 (2020) 2781–2828

DOI: 10.2140/gt.2020.24.2781

Abstract

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 $1$ –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 Göttsche and Kool (Pure Appl. Math. Q. 14 (2018) 467–513) for ranks $2$ and $3$ .

Keywords

Vafa–Witten invariants, monopole contribution, VW invariants

Mathematical Subject Classification 2010

Primary: 14C05, 14D20, 14J80

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

Authors

Ties Laarakker
Imperial College London United Kingdom

Volume 24, issue 6 (2020)