Geometry and Topology seminar
Speaker: Dr. Ishan Banerjee, Ohio State University
Host: Sandip Singh
Title: Monodromy of curves in an algebraic surface
Time, day and date: 9:30:00 AM - 10:30:00 AM, Tuesday, March 17
Venue: Online (Google Meet: https://meet.google.com/jzy-kqch-nzy)
Abstract: Given an algebraic surface X embedded into P^N, we can consider the family of smooth curves in X arising from intersecting a degree d hypersurface in P^N with X. This is a fiber bundle with fibers Riemann surfaces of genus g for some g.

Associated to this family of curves we have a monodromy group contained in the mapping class group of a genus g surface. We prove under some ampleness conditions that if X is simply connected this monodromy group is of finite index (we explicitly determine what it is). This is joint work with Nick Salter.