2018 Thematic Program (III)

Varieties with trivial first Chern class


October 15-19, 2018

W303  School of Mathematics, Sichuan University

[Minicourse II]H.Guenancia1015-1019.png


H. Guenancia (Institut de Mathematiques de Toulouse)


The goal of this course is to explain the proof of a decomposition theorem due to Beauville and Bogomolov which asserts that any compact Kahler manifold with trivial first Chern class admits a finite unramified cover which splits as a product of a torus, Calabi-Yau varieties and irreducible holomorphic symplectic varieties. One of the essential tools of the proof is the existence of a Kahler Ricci-flat metric, guaranteed by Yau's theorem.

Eventually, we will move on to the case of projective varieties with mild singularities and trivial first Chern class, explaining the very recent generalization by Horing and Peternell. Here again, the existence of singular Kahler-Ricci flat metrics is crucial. The proof is much more lengthy, and we will only provide a sketch of if.


1.   A.Beauville, Varietes dont la premiere classe de Chern est nulle, J. Differential Geom. 18 (1983), n4, 755-782

2. A.Horing and T.Peternell, Algebraic integrability of foliations with numerically trivial canonical bundle, ArXiv:1710.06183

3.  D.Greb, H.Guenancia, S.Kebekus, Klt varieties with trivial canonical class - Holonomy, differential forms, and fundamental groups, ArXiv:170401408


Bohui Chen (Sichuan University)

Xiaojun Chen (Sichuan University)

Yuxin Ge (Institut de Mathematiques de Toulouse)

Li Sheng (Sichuan University)


Jean-Pierre Demailly (French Academy of Sciences)

Vincent Guedj (Institut de Mathematiques de Toulouse)

An-Min Li (Sichuan University)

Xiangyu Zhou (Chinese Academy of Sciences)


ANR GRACK project

Institut de Mathematiques de Toulouse

Sichuan University

Tianyuan Fund for Mathematics