Locally conformally Kähler spaces and proper open morphisms

2023/11/24 by Preda, Ovidiu, Stanciu, Miron
#32S45 #53C55 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.14372

Abstract

In this paper, we prove a stability result for the non-Kähler geometry of locally conformally Kähler (lcK) spaces with singularities. Specifically, we find sufficient conditions under which the image of an lcK space by a holomorphic mapping also admits lcK metrics, thus extending a result by Varouchas about Kähler spaces.

Related

• Coverings of locally conformally Kähler complex spaces
• LCK metrics on complex spaces with quotient singularities
• Vaisman theorem for lcK spaces
• Functionals for the Study of LCK Metrics on Compact Complex Manifolds
• Calabi-Yau locally conformally Kähler manifolds