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.
Original language | English |
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Pages (from-to) | 1000-1034 |
Number of pages | 35 |
Journal | European Journal of Mathematics |
Volume | 4 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Sept 2018 |
Keywords
- K3 surfaces
- variations of GIT quotients
- period map
- quartic curves
ASJC Scopus subject areas
- Geometry and Topology
- Algebra and Number Theory