Involutions of curves in abelian surfaces and their Jacobians

2025/04/09 by Honigs, Katrina, Sarmah, Pijush Pratim
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.06502

Abstract

We examine étale covers of genus two curves that occur in the linear system of a polarizing line bundle of type (1,d) on a complex abelian surface. We give results counting fixed points of involutions on such curves as well as decomposing their Jacobians into isogenous products.

Citations

• Decomposable Jacobians
• Hyperelliptic curves on (1,4) polarised abelian surfaces
• Curve counting on abelian surfaces and threefolds

Related

• Characterizing Jacobians of algebraic curves with involution
• The Hesse pencil and polarizations of type (1,3) on Abelian surfaces
• Non-simple polarised abelian surfaces and genus 3 curves with completely decomposable Jacobians
• Abelian surfaces with an automorphism and quaternionic multiplication
• On the Jacobian variety of the Accola-Maclachlan curve of genus four