# Compactifications of the moduli space of plane quartics and two lines

European Journal of Mathematics, Apr 2018

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.

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Patricio Gallardo, Jesus Martinez-Garcia, Zheng Zhang. Compactifications of the moduli space of plane quartics and two lines, European Journal of Mathematics, 2018, 1-35, DOI: 10.1007/s40879-018-0248-7