## Geometry & Topology

### Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups

#### 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.

#### Article information

Source
Geom. Topol., Volume 23, Number 4 (2019), 2051-2124.

Dates
Accepted: 2 December 2018
First available in Project Euclid: 16 July 2019

https://projecteuclid.org/euclid.gt/1563242525

Digital Object Identifier
doi:10.2140/gt.2019.23.2051

Mathematical Reviews number (MathSciNet)
MR3988092

Zentralblatt MATH identifier
07094913

#### Citation

Greb, Daniel; Guenancia, Henri; Kebekus, Stefan. Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups. Geom. Topol. 23 (2019), no. 4, 2051--2124. doi:10.2140/gt.2019.23.2051. https://projecteuclid.org/euclid.gt/1563242525

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