Pseudo-effective adjoint classes and volume in Kahler family with Projective central fiber
Published in Journal 1, 2025
This paper is devoted to the study of the deformation behavior of positivity properties and the volume of adjoint classes in K"ahler families. Building on recent developments in the K"ahler minimal model program, we establish both the deformation openness and closedness of pseudo-effective adjoint classes, assuming that the central fiber is projective with canonical singularities. Furthermore, for a smooth K"ahler family whose central fiber is projective with a big adjoint class, we prove that the volume is constant in family. Finally, using the minimal model theory for K"ahler threefolds, we also demonstrate the deformation invariance of volume and plurigenera for smooth families of K"ahler threefolds, which verifies Siu invariance of plurigenera conjecture in threefold cases.
Download here