Imperial College London
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Professor Richard Thomas FRS

Faculty of Natural Sciences, Department of Mathematics

Royal Society Research Professor (Pure Mathematics)
 
 
 
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Contact

 

richard.thomas Website

 
 
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Location

 

659Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Tanaka:2018:10.4310/PAMQ.2017.v13.n3.a6,
author = {Tanaka, Y and Thomas, RP},
doi = {10.4310/PAMQ.2017.v13.n3.a6},
journal = {Pure and Applied Mathematics Quarterly},
pages = {517--562},
title = {Vafa-Witten invariants for projective surfaces II: semistable case},
url = {http://dx.doi.org/10.4310/PAMQ.2017.v13.n3.a6},
volume = {13},
year = {2018}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - 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≤0we expect our definition coincides with an alternative definition using weighted Euler characteristics. We prove this for degKS<0 here, and it is proved for Sa K3 surface in “Sheaf counting on local K3 surfaces” [D. Maulik and R. P. Thomas, arXiv:1806.02657].For K3 surfaces we calculate the invariants in terms of modular forms which generalise and prove conjectures of Vafa and Witten.
AU  - Tanaka,Y
AU  - Thomas,RP
DO  - 10.4310/PAMQ.2017.v13.n3.a6
EP  - 562
PY  - 2018///
SN  - 1558-8599
SP  - 517
TI  - Vafa-Witten invariants for projective surfaces II: semistable case
T2  - Pure and Applied Mathematics Quarterly
UR  - http://dx.doi.org/10.4310/PAMQ.2017.v13.n3.a6
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000450014600006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - http://hdl.handle.net/10044/1/65189
VL  - 13
ER  -
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