A characterization of surfaces whose universal cover is the bidisk
| dc.creator | Catanese, Fabrizio | |
| dc.creator | Franciosi, Marco | |
| dc.date | 2008-03-20 | |
| dc.date | 2008-03-26 | |
| dc.date.accessioned | 2026-07-07T09:28:15Z | |
| dc.date.available | 2026-07-07T09:28:15Z | |
| dc.description | We 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.description | 12 pages, references added | |
| dc.identifier | https://arxiv.org/abs/0803.3008 | |
| dc.identifier | http://arxiv.org/abs/0803.3008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157385 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14J25, 32 Q 30, 14J29 | |
| dc.title | A characterization of surfaces whose universal cover is the bidisk | |
| dc.type | text |