Time：14:00, Tuesday, November 10 2026
Venue: E14-301
Speaker：Francesco Zucconi, University of Udine
Title：Singular points on Abelian Surfaces
Abstract：We extend to the compact setting certain greatest common divisor (gcd) estimates previously established in the toric framework. Specifically, for an affine curve on the torus $\mathbb{G}_{m}^{2}$ with a fixed Euler characteristic, Corvaja and Zannier proved that the maximal multiplicity of the curve is bounded by an explicit little-o function of its degree. In this paper, we present partial results toward establishing the function field analogue for abelian surfaces. Our main contributions consist of upper bounds for the maximal singularity of an algebraic curve on an abelian surface, expressed in terms of the curve's degree with respect to a given polarization and its total number of singular points.
