What question did this study set out to answer?

The aim is to examine unramified Galois coverings of genus 2 curves and their associated Prym structures.

January 18, 2026

Pryms of ℤ₃×ℤ₃ coverings of genus 2 curves

Key Points

The aim is to examine unramified Galois coverings of genus 2 curves and their associated Prym structures.
Analyzed Prym varieties corresponding to unramified Galois coverings.
Investigated the Prym map for coverings with arbitrary abelian group support.
Established conditions under which the Prym-Torelli theorem holds for these coverings.
Proved that any unramified Galois covering can be reconstructed from its Prym variety.
Demonstrated that the generic fiber of the Prym map is finite unless the abelian group is cyclic of order less than 6.

Abstract

We study unramified Galois Z 3 × Z 3 Z₃ Z₃ -coverings of genus 2 curves and the corresponding Prym varieties and Prym maps. In particular, we prove that any such covering can be reconstructed from its Prym variety, that is, the Prym–Torelli theorem holds for these coverings. We also investigate the Prym map of unramified G G -coverings of genus 2 curves for an arbitrary abelian group G G. We show that the generic fiber of the Prym map is finite unless G G is cyclic of order less than 6.

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