Vaisman manifolds with vanishing first Chern class
Differential Geometry
2023-04-06 v1 Algebraic Geometry
Complex Variables
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.
Keywords
Cite
@article{arxiv.2304.02582,
title = {Vaisman manifolds with vanishing first Chern class},
author = {Nicolina Istrati},
journal= {arXiv preprint arXiv:2304.02582},
year = {2023}
}