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arXiv · 1708.08420

Compactifications of the moduli space of plane quartics and two lines

Patricio Gallardo·Jesus Martinez-Garcia·Zheng Zhang
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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.

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Patricio Gallardo, Jesus Martinez-Garcia, Zheng Zhang. 2017-08-28. Compactifications of the moduli space of plane quartics and two lines. https://doi.org/10.1007/s40879-018-0248-7

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