Compactifications of the moduli space of plane quartics and two lines

Abstract

We study the moduli space of triples $(C,L_1,L_2)$ consisting of quartic curves $C$ and lines $L_1$ and $L_2$. Specifically, we construct and compactify the moduli space in two ways: via geometric invariant theory (GIT) and by using the period map of certain lattice polarized $K3$ surfaces. The GIT construction depends on two parameters $t_1$ and $t_2$ which correspond to the choice of a linearization. For $t_1=t_2=1$ we describe the GIT moduli explicitly and relate it to the construction via $K3$ surfaces.

28 pages, 2 figures. To appear in Eur. J. Math

References in corpus (1)

• Variations of geometric invariant quotients for pairs, a computational approach

Cited by in corpus (1)

• Applications of the moduli continuity method to log K-stable pairs