Gallardo, Patricio and Martinez-Garcia, Jesus and Zhang, Zheng (2018) Compactifications of the moduli space of plane quartics and two lines. European Journal of Mathematics, 4 (3). pp. 1000-1034. DOI https://doi.org/10.1007/s40879-018-0248-7
Gallardo, Patricio and Martinez-Garcia, Jesus and Zhang, Zheng (2018) Compactifications of the moduli space of plane quartics and two lines. European Journal of Mathematics, 4 (3). pp. 1000-1034. DOI https://doi.org/10.1007/s40879-018-0248-7
Gallardo, Patricio and Martinez-Garcia, Jesus and Zhang, Zheng (2018) Compactifications of the moduli space of plane quartics and two lines. European Journal of Mathematics, 4 (3). pp. 1000-1034. DOI https://doi.org/10.1007/s40879-018-0248-7
Abstract
We study the moduli space of triples (C,L₁,L₂) consisting of quartic curves C and lines L₁ and L₂. 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 t₁ and t₂ which correspond to the choice of a linearization. For t₁=t₂=1 we describe the GIT moduli explicitly and relate it to the construction via K3 surfaces.
| Item Type: | Article |
|---|---|
| Additional Information: | 28 pages, 2 figures. To appear in Eur. J. Math |
| Uncontrolled Keywords: | K3 surfaces; Variations of GIT quotients; Period map; Quartic curves |
| Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
| SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
| Depositing User: | Unnamed user with email elements@essex.ac.uk |
| Date Deposited: | 30 Aug 2019 15:56 |
| Last Modified: | 16 Aug 2025 03:26 |
| URI: | http://repository.essex.ac.uk/id/eprint/25196 |
Available files
Filename: Gallardo2018_Article_CompactificationsOfTheModuliSp.pdf
Licence: Creative Commons: Attribution 3.0