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Seminar on Differential Geometry

 

 

Title: Projective klt pairs with nef anti-canonical divisor and RC fibrations

Speaker: Prof. Shin-ichi Matsumura (Tohoku University)

Time: 10:00-11:00, Aug 29, 2018

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).

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