Jacobians of Curves in Abelian Surfaces

Abstract: Every curve has an abelian variety associated to it, called the Jacobian. Poincaré's total reducibility theorem states that any abelian variety is isogenuous to a product of simple abelian varieties. We are interested to know this decomposition for Jacobians of smooth curves in abelian surfaces. Using Kani and Rosen's strikingly simple yet powerful theorem that relates subgroups of automorphism groups with isogeny relations on Jacobians, we will decompose Jacobians of certain curves coming from linear systems of polarizations on abelian surfaces and comment on curve coverings.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca