Monopole contributions to refined Vafa-Witten invariants
Algebraic Geometry
2021-01-06 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1810.00385,
title = {Monopole contributions to refined Vafa-Witten invariants},
author = {Ties Laarakker},
journal= {arXiv preprint arXiv:1810.00385},
year = {2021}
}
Comments
39 pages; many major and minor modifications; added proof of conjecture on universal series A