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Klt
varieties with trivial canonical class: holonomy,
differential forms, and fundamental groups
Daniel Greb, Henri Guenancia and Stefan Kebekus |
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Geometry & Topology 23 (2019) 2051–2124
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Abstract |
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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. |
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Keywords
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
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Mathematical Subject Classification 2010
Primary: 14E30, 14J32, 32J27
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References |
Publication
Received: 6 November 2017
Accepted: 2 December 2018
Published: 17 June 2019
Proposed: Dan Abramovich
Seconded: Richard Thomas, Jim Bryan
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Authors |
| Daniel Greb | ||
| Essener Seminar für Algebraische
Geometrie und Arithmetik Fakultät für Mathematik Universität Duisburg–Essen Essen Germany |
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| http://www.esaga.uni-due.de/daniel.greb | ||
| Henri Guenancia | ||
| Department of Mathematics Stony Brook University Stony Brook, NY United States |
Institut de Mathématiques de
Toulouse Université Paul Sabatier Toulouse France |
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| https://www.math.univ-toulouse.fr/~hguenanc/ | ||
| Stefan Kebekus | ||
| Mathematisches Institut Albert-Ludwigs-Universität Freiburg Freiburg im Breisgau Germany |
Freiburg Institute for Advanced
Studies Freiburg im Breisgau Germany |
University of Strasbourg Institute
for Advanced Study Strasbourg France |
| https://cplx.vm.uni-freiburg.de | ||
