SFU Number Theory and Algebraic Geometry Seminar: Nils Bruin

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.