Kahler spaces with zero first Chern class: Bochner principle, Albanese map and fundamental groups
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK(2022)
摘要
Let X be a compact Kahler space with klt singularities and vanishing first Chern class. We prove the Bochner principle for holomorphic tensors 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-etale 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-etale covers, these are either irreducible Calabi-Yau or irreducible holomorphic symplectic. As an application of these results, we show that if X has dimension four, then it satisfies Campana's Abelianity Conjecture.
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关键词
first chern class,bochner principle,fundamental groups,albanese map
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