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Criteria of isolated weighted homogeneous hypersurface singularities using Logarithmic vector fields
Jihao Liu, Xiping Zhang
We prove a conjecture of da Silva Machado and Seade that characterizes weighted homogeneous isolated hypersurface singularities through the existence of a logarithmic vector field…
Existence of the minimal model program for log canonical generalized pairs
Zhengyu Hu, Jihao Liu
We introduce linearly decomposable (LD) generalized pairs, which serve as a workable substitute for rational decompositions in the non-NQC setting. Using LD generalized pairs, toge…
Dual complexes of qdlt Fano type models and strong complete regularity
Jihao Liu, Konstantin Loginov
We introduce birational strong complete regularity and strong complete regularity, two numerical invariants for pairs of (relative) Fano type. They are defined using variants of qd…
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…
A generalized non-vanishing theorem on surfaces
Jihao Liu, Lingyao Xie
We show that the anti-canonical bundle of any -factorial surface is numerically effective if and only if it is pseudo-effective. To prove this, we establish a numerical…
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…