S. Kebekus - Varieties with vanishing first Chern class

Stefan Kebekus (1) , Jérémy Magnien

1 Mathematisches Institut [Freiburg]

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 irreductibility of holonomy representations and stability of the tangent sheaf are established. As a consequence, we show that up to finite quasi-étale covers, varieties with strongly stable tangent sheaf are either Calabi-Yau (CY) or irreducible holomorphic symplectic (IHS). Finally, finiteness properties of fundamental groups of CY and IHS varieties are established.

Mots clés: Complex analytic and differential geometry 2017; Grenoble; varieties; Chern class

Domaines: Géométrie différentielle [math.DG]

Stefan Kebekus, Jérémy Magnien. S. Kebekus - Varieties with vanishing first Chern class: Complex analytic and differential geometry 2017, Grenoble . 2017. ⟨medihal-01617927⟩