Reconstructing genus 4 curves and applications

We present a method for recovering the canonical model of a genus 4 curve from its theta constants. We describe some applications, such as gluing genus 2 curves, computing examples of explicit modularity for abelian varieties with real multiplication, and computing Jacobians with complex multiplication. As a final example, we discuss work in progress toward explicitly computing an abelian 4-fold of Mumford type. Joint work with Thomas Bouchet, Jeroen Hanselman, and Andreas Pieper.

Sam has also kindly agreed to give a pretalk from 2:00-2:45pm in SC 530. We especially encourage younger students to attend and ask questions! The pretalk will be on genus 4 curves and theta constants.