Li Yi

Li Yi

I am a 3rd year PhD student majoring in birational geometry

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publications

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

Published in arxiv, 2025

This paper is devoted to studying the deformation behavior of pseudo- effective canonical divisors and volumes of adjoint classes in Kähler families. Based on recent developments in the Kähler minimal model program, for (flat) families with fiberwise canonical singularities, we establish the global stability of the pseudo-effectivity of canonical divisors, assuming in addition that one fiber is projective, while the same conclusion for Kähler threefolds is also true without the projectivity assumption of the central fiber. For smooth Kähler families 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 plurigenera for smooth families of Kähler threefolds, thereby confirming Siu’s invariance of plurigenera conjecture in dimension three.

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talks

Attend the ICCM2024

Published:

I attend the 2024 Annual International Congress of Chinese Mathematicians from Jan 03,2025 - Jan 07, 2025.

Families of Kähler spaces

Published:

I will attend the conference on “Families of Kähler spaces” at CIRM Marseille from April 20 - April 26 2025.

teaching