On varieties whose universal cover is a product of curves
| dc.creator | Catanese, Fabrizio | |
| dc.creator | Franciosi, Marco | |
| dc.date | 2008-12-23 | |
| dc.date.accessioned | 2026-07-07T12:21:20Z | |
| dc.date.available | 2026-07-07T12:21:20Z | |
| dc.description | We investigate a necessary condition for a compact complex manifold X of dimension n in order that its universal cover be the Cartesian product $C^n$ of a curve $C = \PP^1 or \HH$: the existence of a semispecial tensor $ω$. A semispecial tensor is a non zero section $ 0 \neq ω\in H^0(X, S^nΩ^1_X (-K_X) \otimes η) $), where $η$ is an invertible sheaf of 2-torsion (i.e., $η^2\cong \hol_X$). We show that this condition works out nicely, as a sufficient condition, when coupled with some other simple hypothesis, in the case of dimension $n= 2$ or $ n= 3$; but it is not sufficient alone, even in dimension 2. In the case of Kähler surfaces we use the above results in order to give a characterization of the surfaces whose universal cover is a product of two curves, distinguishing the 6 possible cases. | |
| dc.description | 22 pages, dedicated to Sommese's 60-th birthday. Greatly improves, expands and supersedes arXiv:0803.3008, of which also corrects a mistake | |
| dc.identifier | https://arxiv.org/abs/0812.4317 | |
| dc.identifier | http://arxiv.org/abs/0812.4317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213333 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14J25, 32Q30, 14J29 | |
| dc.title | On varieties whose universal cover is a product of curves | |
| dc.type | text |