Ce travail comprend deux parties. La premiere expose la structure des varietes
kahleriennes compactes avec cλ—0, suivant des idees de F. Bogomolov [2], et d'autres …

The paper generalizes some of the well-known results for K3 surfaces to higher-dimensional
irreducible symplectic (or, equivalently, compact irreducible hyperkaehler) manifolds. In …

A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by
the isotopies. We compute a mapping class group of a hyperkähler manifold M, showing that …

(0.1) In recent years, the classification theory of algebraic varieties pro-grammed by Iitaka
has been developed a great deal by Ueno, Viehweg, Fu-jita, Kawamata, Kollár (in the order …

We obtain new criteria for a normal projective variety to be projective n-space. Our main
result asserts that a normal projective variety which carries a closed, doubly-dominant …

In this note, we investigate fibre space structures of a projective irreducible symplectic
manifold. We prove that a 2n-cdimensional projective irreducible symplectic manifold admits …

We study the asymptotic behavior of volume forms on a degenerating family of compact
complex manifolds. Under rather general conditions, we prove that the volume forms …

We study a generalization of a conjecture made by Beauville on the Chow ring of hyper-K\"
ahler algebraic varieties. Namely we prove in a number of cases that polynomial …

Let M be an irreducible holomorphically symplectic manifold. We show that all faces of the
Kähler cone of M are hyperplanes H_i orthogonal to certain homology classes, called …

arXiv:math/0606409v1 [math.AG] 16 Jun 2006 Page 1 arXiv:math/0606409v1 [math.AG] 16 Jun
2006 On the Beauville form of the known irreducible symplectic varieties Antonio Rapagnetta …