3 papers
math.AG2026
Beauville--Bogomolov--Fujiki positivity and Moishezonness of complex symplectic manifolds in Fujiki class
Jian Chen
Motivated by the principle that positivity of the Beauville--Bogomolov--Fujiki (BBF) form controls the geometry of hyperkähler manifolds, we study BBF positivity from the perspecti…
math.CV2026
Kahler structure of the total space near a Kahler fiber
Jian Chen
Motivated by the Kodaira-Spencer local stability theorem for Kahler structures and by C. Li's study of Kahler structures on holomorphic submersions between compact complex manifold…
math.AG2025
Criteria for a fiberwise Fujiki/Kahler family to be locally Moishezon/projective
Jian Chen
We utilize the theory of non-Kahler loci by S. Boucksom to construct an integral 2-cohomology class whose restriction to a general fiber is big, and then construct a relatively big…