3 papers
math.AG2026
Polynomial Lower Bounds for Anticanonical Volumes of Weak Fano Surfaces
Pinxian Bie
We prove an explicit lower bound of order for the anticanonical volume of every complex -log canonical weak del Pezzo surface.…
math.AG2026
On the DCC Property of Iitaka Volume with Real Coefficients and Generalised Pairs
Pinxian Bie
We investigate the DCC property of the set of Iitaka volumes of a given set of pairs of varieties. We both generalize previous results of Birkar and Li about usual pairs to the rea…
math.AG2025
Explicit Effective Birationality for Singular Surfaces
Pinxian Bie
We give some explicit upper bounds on the effective birationality of the canonical or anti-canonical system for a singular surface. In particular, we show that for any surface …