Institut de recherche mathématique avancée

Résumé : For projective log canonical pairs (X,B) with nonnegative Iitaka—Kodaira dimension κ, the Iitaka volume vol_κ (K_X+B) measures the asymptotic growth of the pluricanonical systems. In the general type case, it is just the usual notion of volume, and plays a key role in the classification theory. In this talk, I will report on some results about the distribution of the Iitaka volumes of log canonical surfaces and threefolds with intermediate Kodaira dimensions. In particular, we have found the minimal possible Iitaka volume of a projective log canonical surface X with κ(K_X)=1. The talk is based on joint work in progress with Guodu Chen and Jingjun Han.