Computational Algebra Seminar: Swinarski -- Low degree Hilbert stability and curves with automorphisms

Speaker: David Swinarski (University of Georgia)
Title: Low degree Hilbert stability and curves with automorphisms
Time & Place: 3-4pm, Thursday 23 June, Carslaw 173

Abstract: Geometric invariant theory (GIT) has been used to construct many
moduli spaces and birational models of moduli spaces.  Predictions by
Hassett and Keel suggest that one should get interesting models of
$\bar{M}_{g}$ (the moduli space of stable curves) by changing the
parameters of Gieseker’s GIT construction of $\bar{M}_{g}$.  Ian Morrison
and I developed Grobner basis techniques to help us study these new GIT
quotients.  One trick we use relies heavily on the representation
theory of automorphisms of curves.  I’ll explain how we used various
software packages in the original project, and some of the tools I have
implemented or would like to implement in Magma.