Compactifications of the moduli space of plane quartics and two lines

Jesus Martinez-Garcia; Patricio Gallardo; Zheng Zhang

doi:10.1007/s40879-018-0248-7

Compactifications of the moduli space of plane quartics and two lines

Jesus Martinez-Garcia
, Patricio Gallardo
, Zheng Zhang

Department of Mathematical Sciences

Texas A&M University
Washington University in St. Louis

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

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
Pages (from-to)	1000-1034
Number of pages	35
Journal	European Journal of Mathematics
Volume	4
Issue number	3
DOIs	https://doi.org/10.1007/s40879-018-0248-7
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

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10.1007/s40879-018-0248-7Licence: CC BY

Cite this

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title = "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. ",

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AU - Gallardo, Patricio

AU - Zhang, Zheng

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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

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EP - 1034

JO - European Journal of Mathematics

JF - European Journal of Mathematics

IS - 3

ER -

Compactifications of the moduli space of plane quartics and two lines

Abstract

Keywords

ASJC Scopus subject areas

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