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Vafa-Witten invariants for projective surfaces II: semistable case

Abstract:

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.

Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.4310/PAMQ.2017.v13.n3.a6

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More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Worcester College
Thomas, RP More by this author
Japan Society for the Promotion of Science More from this funder
Simons Collaboration More from this funder
Publisher:
International Press Publisher's website
Journal:
Pure and Applied Mathematics Quarterly Journal website
Volume:
13
Issue:
3
Pages:
517–562
Publication date:
2018-11-12
Acceptance date:
2018-05-15
DOI:
EISSN:
1558-8602
ISSN:
1558-8599
Pubs id:
pubs:871236
URN:
uri:50d5854e-274e-4ded-85c8-f76e455bce60
UUID:
uuid:50d5854e-274e-4ded-85c8-f76e455bce60
Local pid:
pubs:871236

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