Work

Vaisman manifolds with vanishing first Chern class

Year: 2025

Type: article

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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1633

Author: Nicolina Istrati

Institution: Université d'Angers

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Award: Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation