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 with complex multiplication over 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.