Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Shin-ichi Matsumura, Tohoku University
Inviter:
Title:
Projective klt pairs with nef anti-canonical divisor and RC fibrations
Time & Venue:
2018.8.29 10:00-11:00 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).