Intersections of the automorphism and p-rank strata inside of \(M_2\)

2025

1. arXiv

   

   Intersections of the automorphism and the Ekedahl-Oort strata in the moduli space of genus two curves

   Alvaro Gonzalez-Hernandez

   arXiv preprint. Comments are welcome!, 2025

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   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.

   @article{Gonzalez-Hernandez2025IntersectionsStrata,
     title = {{Intersections of the automorphism and the Ekedahl-Oort strata in the moduli space of genus two curves}},
     author = {Gonzalez-Hernandez, Alvaro},
     year = {2025},
     pages = {21},
     publisher = {arXiv},
     eprint = {2507.07278},
     journal = {arXiv preprint. Comments are welcome!}
   }