Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(5): 1725-1741

Online first article July 6, 2017      Printed September 30, 2017

https://doi.org/10.4134/BKMS.b160689

Copyright © The Korean Mathematical Society.

The Bogomolov-Prokhorov invariant of surfaces as equivariant cohomology

Evgeny Shinder

University of Sheffield

Abstract

For a complex smooth projective surface $M$ with an action of a finite cyclic group $G$ we give a uniform proof of the isomorphism between the invariant $H^1(G, H^2(M, \Z))$ and the first cohomology of the divisors fixed by the action, using $G$-equivariant cohomology. This generalizes the main result of Bogomolov and Prokhorov \cite{BP}.

Keywords: obstructions to equivariant rationality, equivariant cohomology

MSC numbers: 14J26, 14L30, 55N91

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