Geometry & Topology
- Geom. Topol.
- Volume 23, Number 4 (2019), 2051-2124.
Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups
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.
Geom. Topol., Volume 23, Number 4 (2019), 2051-2124.
Received: 6 November 2017
Accepted: 2 December 2018
First available in Project Euclid: 16 July 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
varieties with trivial canonical divisor klt singularities Kähler–Einstein metrics stability holonomy groups Bochner principle irreducible holomorphic symplectic varieties Calabi–Yau varieties differential forms fundamental groups decomposition
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