Algèbre, géométrie, topologie

Minimal Projective Varieties satisfying 3c2=c12

par Niklas Müller (Essen)

Europe/Paris
Description
It is a classical fact that the Chern classes of any minimal smooth projective surface X satisfy the so-called Bogomolov-Miyaoka-Yau inequality 3c2(X)c12(X)0 and it is known explicitely for which surfaces equality is attained. More generally, if X is a minimal projective variety of dimension n, Miyaoka proved that (3c2(X)c12(X))Hn20 for any ample divisor H on X. In this talk I want to discuss the structure of those varieties X attaining equality. In particular, we will see that abundance holds for such varieties. This is joint work with M. Iwai and S.-I. Matsumura.