Section: New Results

CM Plane Quartics

Participant : Hugo Labrande.

As a by-product of his PhD thesis defended in late 2016, Hugo Labrande contributed to a joint work with several authors, leading to an article [21] that provides examples of smooth plane quartics over $\mathbb{Q}$ with complex multiplication over $\overline{\mathbb{Q}}$ by a maximal order with primitive CM type. Several algorithms are used, in tight connection to the computation of Theta functions which was improved in Labrande's PhD thesis: reduction of period matrices, fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants.