Publications

We show that flips and divisorial contractions preserve the Kähler condition for strongly $\mathbb{Q}$-factorial Kähler generalized klt pairs whose boundary $B + \beta_X$ is big, and we give a criterion for a variety in Fujiki’s class $\mathcal{C}$ to be Kähler. We also prove the existence of small $\mathbb{Q}$-factorializations for generalized klt pairs and of dlt modifications for generalized pairs.

This paper studies the deformation behaviour of pseudo-effective canonical divisors and of volumes of adjoint classes in Kähler families. Building on recent developments in the Kähler minimal model program, we establish, for flat families with fiberwise canonical singularities and one projective fiber, the global stability of pseudo-effectivity of the canonical divisor and of uniruledness; for Kähler threefolds the same conclusion holds without the projectivity assumption on the central fiber. For a smooth Kähler family whose central fiber is projective with a big adjoint class, we show that the volume remains locally constant. Finally, using the (relative) minimal model program for Kähler threefolds, we verify the deformation invariance of volumes of adjoint classes and of plurigenera for smooth families of Kähler threefolds, thereby confirming Siu’s invariance of plurigenera conjecture in dimension three.