BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Plane quartics over Q with complex multiplication Ritzenthaler, Christophe


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

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