3 papers
math.AG2026
The minimal volume of stable surfaces of rank one
Jihao Liu, Wenfei Liu
We determine the minimal volume of a stable surface of rank one, and show that the surface attaining this minimum is unique up to isomorphism. This resolves a conjecture of Alexeev…
math.AG2026
The minimal volume of surfaces of log general type with non-empty non-klt locus
Jihao Liu, Wenfei Liu
We show that the minimal volume of surfaces of log general type, with non-empty non-klt locus on the ample model, is . Furthermore, the ample model achieving the…
math.AG2025
The minimal volume of log surfaces of general type with positive geometric genus
Wenfei Liu
We determine the minimal possible volume of a projective log canonical surface of general type with prescribed positive geometric genus. As applications, we provide effecitive Noet…