Title: Projective klt pairs with nef anti-canonical divisor and RC fibrations
Speaker: Prof. Shin-ichi Matsumura (Tohoku University)
Time: 2018-8-29, 10:00-11:00
Place: N820
Abstract: The famous result of Kollar-Miyaoka-Mori and Campana says that any Fano variety is rationally connected. Hacon-McKernan gave a conjecture which asks a relation between the geometry of rational curves and positivity of nef anti-canonical bundle for projective manifolds with klt singularities. Ejiri-Gongyo recently proved Hacon-McKernan's conjecture. In this talk, I will give a sharper inequality than the conjecture posed by Hacon-McKernan and proved by Ejiri-Gongyo, by using positively curved singular hermitian metrics on direct image sheaves.This is a joint work with Junyan Cao (Institut de Mathematiques de Jussieu).