Abstract for the talk on 25.07.2018 (09:00 h)

Seminar on Nonlinear Algebra

Christophe Ritzenthaler (University de Rennes 1)
Construction of genus 3 curves with complex multiplication over Q

We give examples of smooth plane quartics over Q with complex multiplication over Q by a maximal order with primitive CM type. We describe the required algorithms as we go: these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we discuss some of the reduction properties of the curves that we obtain.