Intersections of the automorphism and the Ekedahl-Oort strata in $M_2$

Fuente: arXiv
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Main Author: Gonzalez-Hernandez, Alvaro
Format: Preprint
Published: 2025
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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