Compactifications of moduli of points and lines in the projective plane
| Autor: | Schaffler, Luca, Tevelev, Jenia |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | Projective duality identifies the moduli spaces $\mathbf{B}_n$ and $\mathbf{X}(3,n)$ parametrizing linearly general configurations of $n$ points in $\mathbb{P}^2$ and $n$ lines in the dual $\mathbb{P}^2$, respectively. The space $\mathbf{X}(3,n)$ admits Kapranov's Chow quotient compactification $\overline{\mathbf{X}}(3,n)$, studied also by Lafforgue, Hacking, Keel, Tevelev, and Alexeev, which gives an example of a KSBA moduli space of stable surfaces: it carries a family of certain reducible degenerations of $\mathbb{P}^2$ with $n$ "broken lines". Gerritzen and Piwek proposed a dual perspective, a compact moduli space parametrizing certain reducible degenerations of $\mathbb{P}^2$ with $n$ smooth points. We investigate the relation between these approaches, answering a question of Kapranov from 2003. Comment: 66 pages. Final version. To appear in International Mathematics Research Notices |
| Databáze: | arXiv |
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