Compactifications of the moduli space of plane quartics and two lines

Jesus Martinez-Garcia, Patricio Gallardo, Zheng Zhang

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1000-1034
Number of pages35
JournalEuropean Journal of Mathematics
Volume4
Issue number3
DOIs
Publication statusPublished - 1 Sep 2018

Fingerprint

Geometric Invariant Theory
Quartic
Compactification
Moduli Space
K3 Surfaces
Line
Linearization
Two Parameters
Modulus
Curve

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology
  • Algebra and Number Theory

Cite this

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

In: European Journal of Mathematics, Vol. 4, No. 3, 01.09.2018, p. 1000-1034.

Research output: Contribution to journalArticle

Martinez-Garcia, Jesus ; Gallardo, Patricio ; Zhang, Zheng. / Compactifications of the moduli space of plane quartics and two lines. In: European Journal of Mathematics. 2018 ; Vol. 4, No. 3. pp. 1000-1034.
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