A decomposition theorem for singular K\"ahler spaces with trivial first Chern class of dimension at most four

Patrick Graf

doi:10.5802/afst.1757

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arXiv · 2101.06764

A decomposition theorem for singular K\"ahler spaces with trivial first Chern class of dimension at most four

Patrick Graf

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Abstract

Let $X$ be a compact K\"ahler fourfold with klt singularities and vanishing first Chern class, smooth in codimension two. We show that $X$ admits a Beauville-Bogomolov decomposition: a finite quasi-\'etale cover of $X$ splits as a product of a complex torus and singular Calabi-Yau and irreducible holomorphic symplectic varieties. We also prove that $X$ has small projective deformations and the fundamental group of $X$ is projective. To obtain these results, we propose and study a new version of the Lipman-Zariski conjecture.

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Patrick Graf. 2021-01-17. A decomposition theorem for singular K\"ahler spaces with trivial first Chern class of dimension at most four. https://doi.org/10.5802/afst.1757

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