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April 8, 2026Nagoya Mathematical Journal0 citationsOpen Access

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

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KCKevin ChangDDDušan DragutinovićSGSteven R. Groen

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.

Abstract

Abstract In this article, we investigate the p -rank stratification of the moduli space of curves of genus g that admit a double cover to a fixed elliptic curve E in characteristic p>2. We show that the closed p -rank strata of this moduli space are equidimensional of the expected dimension. We also show the existence of a smooth double cover of E of all the possible values of the p -rank on this moduli space.

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Cite This Study

Chang et al. (2026) studied this question.

synapsesocial.com/papers/69d5f13674eaea4b11a7ab45https://doi.org/10.1017/nmj.2026.10107
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