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arXiv · 2410.20291

Complete Families of Generic Covers of Elliptic Curves

Gabriel Bujokas·Anand Patel
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Abstract

We introduce and motivate a conjecture about the existence of complete, 1-dimensional families of covers of an elliptic curve. If the conjecture holds, then it would imply a uniform lower bound of 5 for slope of the moduli space of curves. If the conjecture fails, this would itself be an interesting phenomenon worthy of explanation.

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Gabriel Bujokas, Anand Patel. 2024-10-26. Complete Families of Generic Covers of Elliptic Curves. https://doi.org/10.1112/mod.2025.10010

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