Vaisman manifolds with vanishing first Chern class

  • Nicolina Istrati

    Université d’Angers, Angers, France
Vaisman manifolds with vanishing first Chern class cover
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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.

Cite this article

Nicolina Istrati, Vaisman manifolds with vanishing first Chern class. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1633