Algebraic Geometry Seminar: "An obstruction for sections of universal hyperelliptic curves"
Abstract: The universal hyperelliptic curve of genus g is the restriction of the universal curve of genus g to the locus of hyperelliptic curves in the moduli stack of proper smooth curves of genus g. It follows from the work of Earle and Kra (1975) that the universal hyperelliptic curve has no sections when g is greater than or equal to 2. Their proof is based on Teichmüller theory. In this talk, I will explain there is a topological obstruction for the existence of sections of the universal hyperelliptic curve when g is greater than or equal to 3.
Host: Matt Kerr