Construction of genus 3 curves with complex multiplication over Q

  • Christophe Ritzenthaler (University de Rennes 1)
E1 05 (Leibniz-Saal)


We give examples of smooth plane quartics over Q with complex multiplication over \bar{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.

Mirke Olschewski

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