Lingyao Xie

collaborators

7 papers

math.AG2026

On the KÃ¤hler MMP and the transcendental base-point-free theorem

Christopher Hacon, Lingyao Xie

In this article, we establish the minimal model program for big gklt KÃ¤hler pairs, and in particular we prove Tosatti's transcendental base-point-free conjecture.

math.AG2026

Minimal model program for algebraically integrable foliations and generalized pairs

Guodu Chen, Jingjun Han, Jihao Liu +1

Using techniques from the theory of foliations, we establish the cone theorem and the contraction theorem for lc generalized pairs in full generality, and meanwhile develop the min…

math.AG2025

Variation of algebraically integrable adjoint foliated structures

Paolo Cascini, Jihao Liu, Fanjun Meng +2

Given a canonical algebraically integrable foliation on a klt projective variety, we study the variation of the ample models of the associated adjoint foliated structures with resp…

math.AG2025

Boundedness of complements for generalized pairs

Guodu Chen, Jingjun Han, Yang He +1

We prove the boundedness of complements for Fano type generalized pairs (with the boundary coefficient set $[0, 1]$ ) after Shokurov.

math.AG2025

Minimal model program for algebraically integrable foliations on klt varieties

Jihao Liu, Fanjun Meng, Lingyao Xie

For lc algebraically integrable foliations on klt varieties, we prove the base-point-freeness theorem, the contraction theorem, and the existence of flips. The first result resolve…

math.AG2025

The extension of numerically trivial divisors on a family

Lingyao Xie

Let $f : X \to S$ be a projective morphism of normal varieties. Assume $U$ is an open subset of $S$ and $L_{U}$ is a $Q$ -divisor on $X_{U} := X \times_{S} U$ such that $L_{U} \equiv_{U} 0$ …