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Vafa-Witten invariants for projective surfaces I: stable case

Abstract:

On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $ \mathbb{C}^*$ action with compact fixed locus. Applying virtual localisation we define invariants constant under deformations. When the vanishing theorem of Vafa-Witten holds, the result is the (signed) Euler characteristic of the moduli space of instantons. In general there are o...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1090/jag/738

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More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Worcester College
Role:
Author
More from this funder
Funding agency for:
Tanaka, Y
Grant:
SimonsCollaborationGrant on“SpecialholonomyinGeometry,Analysis
Physics”
More from this funder
Funding agency for:
Tanaka, Y
Grant:
SimonsCollaborationGrant on“SpecialholonomyinGeometry,Analysis
Physics”
Publisher:
American Mathematical Society Publisher's website
Journal:
Journal of Algebraic Geometry Journal website
Publication date:
2019-10-23
Acceptance date:
2018-11-22
DOI:
EISSN:
1534-7486
ISSN:
1056-3911
Source identifiers:
945778
Pubs id:
pubs:945778
UUID:
uuid:38a2db78-54db-414a-8161-23e14c3ef2d3
Local pid:
pubs:945778
Deposit date:
2018-11-22

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