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September 24, 2025Open Access

On the Prym map of degree 4 cyclic covers of genus 2 curves

Key Points

Non-empty fibers of the Prym map are isomorphic to intersections of an elliptic normal curve in projective space.
The study identifies new descriptions of the space of degree 4 étale cyclic covers of genus 2 curves.
Equations of elliptic and hyperelliptic curves arising from these degree 4 covers are derived.
Two exceptional fibers in the Prym map are noted to be the only exceptions to the isomorphism.

Abstract

In this paper, we study the Prym map associated to degree 4 étale cyclic covers of genus 2 curves. We show that its non-empty fibers, apart from two exceptional fibers, are isomorphic to the intersection of an elliptic normal curve in P³ with an affine space A³ P³. Moreover, we obtain a new description of the space of degree 4 étale cyclic covers of genus 2 curves R₂⁴ and find equations of elliptic and hyperelliptic curves arising from such covers.

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Cite This Study

Anatoli Shatsila (Thu,) studied this question.

synapsesocial.com/papers/68d6e1248b2b6861e4c3f705 https://doi.org/https://doi.org/10.48550/arxiv.2508.20838

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