Time：14:00-16:00, Wednesday, June 3 2026
Venue：E14-116
Speaker: Wenfei Liu, Xiamen University
Title：The volumes of stable surfaces: minimum and accumulation points
Abstract: Stable surfaces are the two‑dimensional analogs of stable curves, arising naturally in the compactification of the moduli space of smooth surfaces of general type. The volume (self‑intersection of the canonical divisor) generalizes the genus of a curve. Unlike the genus, which is always an integer, the volumes of stable surfaces are rational numbers with no uniform bound on denominators. A deep theorem of Valery Alexeev shows that the set of such volumes satisfies the descending chain condition (DCC); nevertheless, it does have accumulation points. Hence, describing this set requires understanding both the minimal possible volume and the accumulation points.
The talk is divided into two parts. The first hour, accessible to undergraduates, introduces stable curves, stable surfaces, and the notion of volume through concrete examples. It explains the DCC property and why accumulation points arise. The second hour, aimed at researchers, surveys recent progress on the minimal volume and the accumulation points of the volume set.
