Jacobians of genus 4 curves that are (2,2)-decomposable

Abstract: Decomposable abelian varieties, and particularly decomposable Jacobians, have a long history; mainly in the form of formulas to compute hyperelliptic integrals in terms of elliptic ones.

The first case where one can have a decomposable Jacobian without elliptic factors is for genus 4: one could have one that is isogenous to the product of two genus 2 Jacobians. Interestingly, though, not all four-dimensional abelian varieties (not even the principally polarized ones) are Jacobians. Classifying which genus 2 Jacobians can be glued together to yield a Jacobian of a genus 4 curve leads to some very interesting geometry on the Castelnuovo-Richmond-Igusa quartic threefold. We will introduce the requisite geometry and sketch some interesting results that follow.

This is joint work with Avinash Kulkarni.

There will be an informal pre-seminar for graduate students at 3pm.

algebraic geometrynumber theory

Audience: researchers in the discipline

( paper )

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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

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