A characterization of surfaces whose universal cover is the bidisk

dc.creatorCatanese, Fabrizio
dc.creatorFranciosi, Marco
dc.date2008-03-20
dc.date2008-03-26
dc.date.accessioned2026-07-07T09:28:15Z
dc.date.available2026-07-07T09:28:15Z
dc.descriptionWe show that the universal cover of a compact complex surface $X$ is the bidisk $\HH \times \HH$, or $X$ is biholomorphic to $\PP^1 \times \PP^1$, if and only if $K_X^2 > 0$ and there exists an invertible sheaf $η$ such that $η^2\cong \hol_X$ and $H^0(X, S^2Ω^1_X (-K_X) \otimes η) \neq 0$. The two cases are distinguished by the second plurigenus, $P_2(X)\geq 2$ in the former case, $P_2(X)= 0$ in the latter. We also discuss related questions.
dc.description12 pages, references added
dc.identifierhttps://arxiv.org/abs/0803.3008
dc.identifierhttp://arxiv.org/abs/0803.3008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157385
dc.subjectAlgebraic Geometry
dc.subjectComplex Variables
dc.subject14J25, 32 Q 30, 14J29
dc.titleA characterization of surfaces whose universal cover is the bidisk
dc.typetext

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