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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}.
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참고문헌 (12)
참고문헌 신청
D. Abramovich / 2002 / Torification and factorization of birational maps / J. Amer. Math. Soc 15(3):531~572
M. A. Armstrong / 1968 / The fundamental group of the orbit space of a discontinuous group / Proc. Cambridge Philos. Soc 64:299~301
M. F. Atiyah / 1961 / Character and cohomology of finite groups / Inst. Hautes tudes Sci. Publ. Math (9):23~64
F. Bogomolov / 2013 / On stable conjugacy of finite subgroups of the plane Cremona group. I / Cent. Eur. J. Math 11(12):2099~2105
A. Borel / 1960 / Seminar on transformation groups / Princeton University Press
M. A. Armstrong / 1968 / The fundamental group of the orbit space of a discontinuous group / Proc. Cambridge Philos. Soc 64:299~301
M. F. Atiyah / 1961 / Character and cohomology of finite groups / Inst. Hautes tudes Sci. Publ. Math (9):23~64
F. Bogomolov / 2013 / On stable conjugacy of finite subgroups of the plane Cremona group. I / Cent. Eur. J. Math 11(12):2099~2105
A. Borel / 1960 / Seminar on transformation groups / Princeton University Press
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