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math.AG2026
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…
math.AG2026
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…
math.AG2026
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…