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.
"Ekedahl–Oort strata on the moduli space of curves of genus four." Rocky Mountain J. Math. 50 (2) 747 - 761, April 2020. https://doi.org/10.1216/rmj.2020.50.747