Honors Thesis Presentation: "Compactifying the Moduli Space of Picard Curves"

Abstract: We construct and compactify the moduli space of Picard curves, which may be realized as either plane quartics, triple covers of the projective line with five branch points, or compact genus three surfaces. We classify singularities and resolve them by way of stable and semi-stable reduction. We then produce an isomorphism from the GIT compactification, which is a quotient of a parameter space by a reductive group, to the Baily-Borel compactification, which is a quotient of a hermitian symmetric space by a discrete subgroup of automorphisms. 

Hosts: Matt Kerr and Patricio Gallardo