Yi Li

Yi Li

PhD candidate in birational geometry

Posts by Collection

portfolio

publications

On Pseudo-Effectivity and Volumes of Adjoint Classes in Kähler Families with Projective Central Fiber

Published in arXiv:2602.04158, 2026

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.

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Fujiki Class 𝒞 Varieties and a Kähler Criterion

Published in arXiv:2608.20588, 2026

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.

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Aspects of Deformation Invariance of Plurigenera of Kähler Varieties

Published in arXiv:2610.17817, 2026

We study several aspects of deformation invariance of plurigenera in Kähler families over a smooth curve. First, for a relatively flat coherent sheaf, we characterize local constancy of fiberwise cohomology dimension by equivalent conditions in terms of extension, base change, torsion freeness of higher direct images, and the vanishing of jumping classes. Then, combining this criterion with the Kähler minimal model program, we prove invariance of plurigenera for Kähler families of threefolds whose central fiber has canonical singularities, and for smooth Kähler families of maximal Albanese dimension. We also establish deformation invariance of log plurigenera when the central fiber is projective, and is of log general type. We prove the invariance of higher cohomological plurigenera assuming that the canonical bundle of the total space is semipositive. Finally, we extend Z. Li–Z. Wang’s deformation invariance result for generalized polarized pairs with abundant nef parts from projective families to Moishezon families.

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talks

Families of Kähler Spaces

Published:

I attended the conference Families of Kähler Spaces at CIRM Marseille, 20–26 April 2025.

teaching