中央研究院數學研究所

Number Theory Seminar

Algebraic Hyperbolicity over Function Fields

2025/12/19 (Fri.) 13:30~14:30

Date : 2025/12/19 (Fri.) 13:30~14:30
Location : Seminar Room 617, Institute of Mathematics (NTU Campus)
Speaker : Zheng Xiao (University of Colorado Boulder)
Organizer : Julie Tzu-Yueh Wang (AS)
Abstract : In this talk I will present new degeneracy results for integral points on smooth projective surfaces over function fields, focusing on the complement of three effective divisors in general position. Under mild hypotheses allowing, we show that any set of (D, S)-integral points is forced either to lie in a proper Zariski-closed subset or to have uniformly bounded height. In particular, the complement of such a divisor configuration is of log general type.
If time permits, I will also discuss an extension of these methods to higher dimensions, yielding analogous hyperbolicity and degen-eracy statements for the complements of n+ 1 divisors in general position on an ,n-dimensional variety.