### Abstract

Original language | English |
---|---|

Pages (from-to) | 1000-1034 |

Number of pages | 35 |

Journal | European Journal of Mathematics |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Sep 2018 |

### Fingerprint

### Keywords

- K3 surfaces
- variations of GIT quotients
- period map
- quartic curves

### ASJC Scopus subject areas

- Geometry and Topology
- Algebra and Number Theory

### Cite this

*European Journal of Mathematics*,

*4*(3), 1000-1034. https://doi.org/10.1007/s40879-018-0248-7

**Compactifications of the moduli space of plane quartics and two lines.** / Martinez-Garcia, Jesus; Gallardo, Patricio; Zhang, Zheng.

Research output: Contribution to journal › Article

*European Journal of Mathematics*, vol. 4, no. 3, pp. 1000-1034. https://doi.org/10.1007/s40879-018-0248-7

}

TY - JOUR

T1 - Compactifications of the moduli space of plane quartics and two lines

AU - Martinez-Garcia, Jesus

AU - Gallardo, Patricio

AU - Zhang, Zheng

PY - 2018/9/1

Y1 - 2018/9/1

N2 - 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.

AB - 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.

KW - K3 surfaces

KW - variations of GIT quotients

KW - period map

KW - quartic curves

UR - http://www.scopus.com/inward/record.url?scp=85052992993&partnerID=8YFLogxK

U2 - 10.1007/s40879-018-0248-7

DO - 10.1007/s40879-018-0248-7

M3 - Article

VL - 4

SP - 1000

EP - 1034

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

IS - 3

ER -