Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

KÄHLER SPACES WITH ZERO FIRST CHERN CLASS: BOCHNER PRINCIPLE, FUNDAMENTAL GROUPS, AND THE KODAIRA PROBLEM

Abstract : Let X be a compact Kähler space with klt singularities and vanishing first Chern class. We prove the Bochner principle for holomorphic ten-sors on the smooth locus of X: any such tensor is parallel with respect to the singular Ricci-flat metrics. As a consequence, after a finite quasi-étale cover X splits off a complex torus of the maximum possible dimension. We then proceed to decompose the tangent sheaf of X according to its holonomy representation. In particular, we classify those X which have strongly stable tangent sheaf: up to quasi-étale covers, these are either Calabi-Yau or irreducible holomorphic symplectic. Several applications of these results are given, the strongest ones of which apply in dimension four. In this case, we prove Campana's Abelianity Conjecture for X. If in addition X has only algebraic singularities then a cover of X admits small projective deformations and the Beauville-Bogomolov Decomposition Theorem holds for X.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [58 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02936352
Contributor : Benoît Claudon <>
Submitted on : Friday, September 11, 2020 - 11:12:54 AM
Last modification on : Wednesday, October 14, 2020 - 4:07:36 AM

Files

bochner.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02936352, version 1

Citation

Benoît Claudon, Patrick Graf, Henri Guenancia, Philipp Naumann. KÄHLER SPACES WITH ZERO FIRST CHERN CLASS: BOCHNER PRINCIPLE, FUNDAMENTAL GROUPS, AND THE KODAIRA PROBLEM. 2020. ⟨hal-02936352⟩

Share

Metrics

Record views

9

Files downloads

23