The p -rank stratification of the moduli space of double covers of a fixed elliptic curve

Key Points

• The research aims to explore the p-rank stratification of the moduli space related to double covers of elliptic curves.
• Analyzed the moduli space of curves of genus g with double covers of a fixed elliptic curve.
• Investigated characteristics of closed p-rank strata.
• Demonstrated smooth double covers for all p-rank values.
• Closed p-rank strata were found to be equidimensional with the expected dimension.
• Existence of a smooth double cover of the elliptic curve for all possible p-rank values was established.