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BibTex format

@article{Tanaka:2020:jag/738,
author = {Tanaka, Y and Thomas, RP},
doi = {jag/738},
journal = {Journal of Algebraic Geometry},
pages = {603--668},
title = {Vafa-Witten invariants for projective surfaces I: stable case},
url = {http://dx.doi.org/10.1090/jag/738},
volume = {29},
year = {2020}
}

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TY  - JOUR
AB  - 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 ∗ 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 other, rational, contributions. Calculations of these on surfaces with positive canonical bundle recover the first terms of modular forms predicted by Vafa and Witten.
AU  - Tanaka,Y
AU  - Thomas,RP
DO  - jag/738
EP  - 668
PY  - 2020///
SN  - 1534-7486
SP  - 603
TI  - Vafa-Witten invariants for projective surfaces I: stable case
T2  - Journal of Algebraic Geometry
UR  - http://dx.doi.org/10.1090/jag/738
UR  - http://arxiv.org/abs/1702.08487v4
UR  - https://www.ams.org/journals/jag/0000-000-00/S1056-3911-2019-00738-1/
UR  - http://hdl.handle.net/10044/1/64607
VL  - 29
ER  -

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