Vaisman manifolds with vanishing first Chern class

Nicolina Istrati

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arXiv · 2304.02582

Vaisman manifolds with vanishing first Chern class

Nicolina Istrati

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Abstract

Compact Vaisman manifolds with vanishing first Chern class split into three categories, depending on the sign of the Bott-Chern class. We show that Vaisman manifolds with non-positive Bott-Chern class admit canonical metrics, are quasi-regular and are stable under deformations. We also show that Calabi-Yau Vaisman manifolds satisfy a version of the Beauville-Bogomolov decomposition and have torsion canonical bundle. Finally, we prove a general result concerning the behaviour of the automorphism group of a complex manifold under deformations.

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Nicolina Istrati. 2023-04-05. Vaisman manifolds with vanishing first Chern class. https://arxiv.org/abs/2304.02582

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