Geometry & Topology Seminar: Singular Fibers in Families of Algebraic Curves

Kodaira gave a classification of singular fibers that can arise in algebraic families of genus 1 curves. This plays an important role in the symplectic topology of elliptic fibrations, where, via Harer-Kas-Kirby, one connects the symplectic topology of a configuration of curves to a monodromy factorization within the genus 1 mapping class group. I'll discuss a project to generalize this to families of genus 2 curves utilizing a classification by Namikawa and Ueno. These families were also studied by Matsumoto-Montesinos in the context of 3-manifolds and surface automorphisms. There is an analytic issue in applying their work to the question at hand and our methods bypass this. This is joint work with Sumeyra Sakalli.

Host: Minh Nguyen