Intersections of the automorphism and the Ekedahl-Oort strata in $M_2$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913068378750976 |
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| author | Gonzalez-Hernandez, Alvaro |
| author_facet | Gonzalez-Hernandez, Alvaro |
| contents | We compute the intersections between the automorphism strata and the pullback by the Torelli map of the Ekedahl-Oort strata inside the moduli space of genus two curves. We first describe explicitly which possible automorphism groups a genus two curve can have over a field of positive characteristic, and parametrise the families of curves with a prescribed automorphism group. Then, we describe an algorithm to compute the strata of genus two curves whose Jacobian variety has a fixed Ekedahl-Oort type. Finally, we compute the dimension and number of irreducible components of the intersections between the strata. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersections of the automorphism and the Ekedahl-Oort strata in $M_2$ Gonzalez-Hernandez, Alvaro Algebraic Geometry Number Theory 11G15, 11G20, 14K10 (Primary), 11G10, 14G17, 14K15 (Secondary) We compute the intersections between the automorphism strata and the pullback by the Torelli map of the Ekedahl-Oort strata inside the moduli space of genus two curves. We first describe explicitly which possible automorphism groups a genus two curve can have over a field of positive characteristic, and parametrise the families of curves with a prescribed automorphism group. Then, we describe an algorithm to compute the strata of genus two curves whose Jacobian variety has a fixed Ekedahl-Oort type. Finally, we compute the dimension and number of irreducible components of the intersections between the strata. |
| title | Intersections of the automorphism and the Ekedahl-Oort strata in $M_2$ |
| topic | Algebraic Geometry Number Theory 11G15, 11G20, 14K10 (Primary), 11G10, 14G17, 14K15 (Secondary) |
| url | https://arxiv.org/abs/2507.07278 |