Title preseminar: Stable maps to projective varieties and quotient stacks
Abstract preseminar: I will introduce the moduli space of stable maps from families of curves to a fixed projective variety. I will explain briefly what quotient stacks are.
Title seminar: Stable maps to quotient stacks with a properly stable point
Abstract seminar: Given the construction of a moduli space of curves, it is natural to ask if one can construct a moduli space of pairs consisting of a curve C together with some extra data. When this extra data is parametrized by a moduli space M, this corresponds to constructing a moduli space of maps from curves to M. I will present a compactification of the moduli space of maps to certain moduli spaces M, via the example of M being the GIT moduli space of binary forms of degree 2n. This leads to a compactification of the moduli space of fibrations f: (X,D) \to C, where each fiber of f is the projective line with a GIT-semistable configuration of 2n points. This is a joint work with Andrea Di Lorenzo.