A Characterization of Surfaces Whose Universal Cover Is the Bidisk
نویسندگان
چکیده
We show that the universal cover of a compact complex surface X is the bidisk H × H, or X is biholomorphic to P × P, if and only if K X > 0 and there exists an invertible sheaf η such that η 2 ∼= OX and H0(X,S2Ω1X(−KX) ⊗ η) 6= 0. The two cases are distinguished by the second plurigenus, P2(X) ≥ 2 in the former case, P2(X) = 0 in the latter. We also discuss related questions.
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