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EnglishWe 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 = P1or H: the existence of a semispecial tensor ω. A semispecial tensor is a non zero section ω ∈ H0(X, SnΩ1 (−K)⊗η)), where η is an invertible sheaf of 2-torsion (i.e., η^2 = OX). 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 K¨ahler 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.
| Titolo: | On varieties whose universal cover is a product of curves | |
| Autori interni: | ||
| Anno del prodotto: | 2009 | |
| Abstract: | 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 = P1or H: the existence of a semispecial tensor ω. A semispecial tensor is a non zero section ω ∈ H0(X, SnΩ1 (−K)⊗η)), where η is an invertible sheaf of 2-torsion (i.e., η^2 = OX). 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 K¨ahler 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. | |
| Handle: | http://hdl.handle.net/11568/131492 | |
| ISBN: | 9780821847466 | |
| Appare nelle tipologie: | 4.1 Contributo in Atti di convegno |
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