Eine Anwendung des Satzes von Calabi-Yau auf Familien kompakter komplexer Mannigfaltigkeiten.
In this paper we compute the Poincaré-Hodge polynomial of a symmetric product of a compact kähler manifold, following the method used by Macdonald, in the topological case, to compute the Poincaré polynomial of a compact polyhedron, and we give some applications, in particular to the case of curves.
We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.
We construct isotrivial and non-isotrivial elliptic curves over with an arbitrarily large set of separable integral points. As an application of this construction, we prove that there are isotrivial log-general type varieties over with a Zariski dense set of separable integral points. This provides a counterexample to a natural translation of the Lang-Vojta conjecture to the function field setting. We also show that our main result provides examples of elliptic curves with an explicit and arbitrarily...