Abstract
We investigate the holonomy group of singular Kähler–Einstein metrics on klt varieties with numerically trivial canonical divisor. Finiteness of the number of connected components, a Bochner principle for holomorphic tensors, and a connection between irreducibility of holonomy representations and stability of the tangent sheaf are established. As a consequence, known decompositions for tangent sheaves of varieties with trivial canonical divisor are refined. In particular, we show that up to finite quasi-étale covers, varieties with strongly stable tangent sheaf are either Calabi–Yau or irreducible holomorphic symplectic. These results form one building block for Höring and Peternell’s recent proof of a singular version of the Beauville–Bogomolov decomposition theorem.
Citation
Daniel Greb. Henri Guenancia. Stefan Kebekus. "Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups." Geom. Topol. 23 (4) 2051 - 2124, 2019. https://doi.org/10.2140/gt.2019.23.2051
Information