Title: Limits of plane curves via stacky branched covers
Speaker: Anand Deopurkar (Columbia University)
Abstract: One of the easiest ways of writing down an algebraic curve is as the zero locus of a polynomial function on the plane. For generic values of the coefficients of the polynomial, the zero locus will be a smooth curve, representing a point in the moduli space of curves. But what happens as the coefficients specialize? Can we describe the limits of smooth plane curves in the Deligne-Mumford compactification of the moduli space of all curves? I will describe an explicit and complete answer to this old question in the first non-trivial case: plane quintics. The solution will use stacky curves and will also explain a web of inter-relations between special 4-gonal and 3-gonal curves described by Vakil.
Seminar URL: https://research.math.osu.edu/agseminar/
