Reduction type of genus-3 curves in a special stratum of their moduli space
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913459974701056 |
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| author | Bouw, Irene Coppola, Nirvana Kılıçer, Pınar Kunzweiler, Sabrina García, Elisa Lorenzo Somoza, Anna |
| author_facet | Bouw, Irene Coppola, Nirvana Kılıçer, Pınar Kunzweiler, Sabrina García, Elisa Lorenzo Somoza, Anna |
| contents | We study a 3-dimensional stratum $\mathcal{M}_{3,V}$ of the moduli space $\mathcal{M}_3$ of curves of genus $3$ parameterizing curves $Y$ that admit a certain action of $V= C_2\times C_2$. We determine the possible types of the stable reduction of these curves to characteristic different from $2$. We define invariants for $\mathcal{M}_{3,V}$ and characterize the occurrence of each of the reduction types in terms of them. We also calculate the $j$-invariant (resp. the Igusa invariants) of the irreducible components of positive genus of the stable reduction of $Y$ in terms of the invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_07633 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Reduction type of genus-3 curves in a special stratum of their moduli space Bouw, Irene Coppola, Nirvana Kılıçer, Pınar Kunzweiler, Sabrina García, Elisa Lorenzo Somoza, Anna Algebraic Geometry Number Theory 14H10, 14H50, 14H25, 11G20, 14Q05, We study a 3-dimensional stratum $\mathcal{M}_{3,V}$ of the moduli space $\mathcal{M}_3$ of curves of genus $3$ parameterizing curves $Y$ that admit a certain action of $V= C_2\times C_2$. We determine the possible types of the stable reduction of these curves to characteristic different from $2$. We define invariants for $\mathcal{M}_{3,V}$ and characterize the occurrence of each of the reduction types in terms of them. We also calculate the $j$-invariant (resp. the Igusa invariants) of the irreducible components of positive genus of the stable reduction of $Y$ in terms of the invariants. |
| title | Reduction type of genus-3 curves in a special stratum of their moduli space |
| topic | Algebraic Geometry Number Theory 14H10, 14H50, 14H25, 11G20, 14Q05, |
| url | https://arxiv.org/abs/2003.07633 |