Pryms of ℤ₃×ℤ₃ coverings of genus 2 curves
Abstract
We study unramified Galois Z 3 × Z 3 \mathbb {Z}_3 \times \mathbb {Z}_3 -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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Mathematics and Applications
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 4
- Pages
- 1433–1451
- Publication date
- 16 January 2026
- Language
- EN