Vafa-Witten invariants for projective surfaces II: semistable case
We propose a definition of Vafa-Witten invariants counting semistable Higgs pairs on a polarised surface. We use virtual localisation applied to Mochizuki/Joyce-Song pairs.
For KS ≤ 0 we expect our definition coincides with an alternative definition using weighted Euler characteristics. We prove this for degKS < 0 here, and it is proved for S a K3 surface in [MT].
For K3 surfaces we calculate the invariants in terms of modular forms which generalise and prove conjectures of Vafa and Witten.
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- Pure and Applied Mathematics Quarterly Journal website
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- © by International Press of Boston, Inc. All rights reserved. This is the accepted manuscript version of the article. The final version is available online from the International Press at: http://dx.doi.org/10.4310/PAMQ.2017.v13.n3.a6
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