2023/02/14 by Chi Li, Li, Chi
Mathematics · #Geometry and complex manifolds #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2302.07220
In this short paper, for any holomorphic submersion π: X→ B, we derive a criterion for X to have Kähler structures. This criterion generalizes Blanchard's criterion for a special class of isotrivial holomorphic submersions. We use this criterion to answer a question of Harvey-Lawson in the case of fiber dimension one. As the main application, we prove that the existence of Hermitian-Symplectic structures on certain class of holomorphic submersions with Kähler fibers and Kähler bases implies that the total spaces are Kähler. This class includes isotrivial submersions and torus fibrations.