Vaisman manifolds with vanishing first Chern class

2023/04/05 by Istrati, Nicolina · 3 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.02582

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.

Cited by

• Non-Kähler Calabi-Yau manifolds and holomorphic geometric structures
• Calabi-Yau locally conformally Kähler manifolds
• An Aubin-Yau theorem for transversally Kähler foliations

Related

• Bott-Chern cohomology of compact Vaisman manifolds
• Kähler manifolds with positive first Chern class and mirrors of rigid Calabi-Yau manifolds
• Approximation results for compact Vaisman manifolds
• A note on compatibility of special Hermitian structures
• Remarks on the Chern classes of Calabi-Yau moduli