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

Alvaro Gonzalez-Hernandez

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arXiv · 2507.07278

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

Alvaro Gonzalez-Hernandez

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Abstract

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.

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Alvaro Gonzalez-Hernandez. 2025-07-09. Intersections of the automorphism and the Ekedahl-Oort strata in $M_2$. https://arxiv.org/abs/2507.07278

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