## Ekedahl-Oort strata on the moduli space of curves of genus four.(English)Zbl 1469.11209

Summary: We study the induced Ekedahl-Oort stratification on the moduli of curves of genus 4 in positive characteristic by computing the de Rham cohomology of curves. For moduli space of hyperelliptic curves of genus 4 in characteristic 3, we determine the dimension and reducibility of Ekedahl-Oort strata. For moduli space of curves of genus 4 in odd characteristic, we show the existence of certain Ekedahl-Oort strata and discuss the existence of superspecial curves.

### MSC:

 11G20 Curves over finite and local fields 14F40 de Rham cohomology and algebraic geometry 14H05 Algebraic functions and function fields in algebraic geometry 14H40 Jacobians, Prym varieties
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### References:

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