Siegel modular forms of degree three and invariants of ternary quartics

Reynald Lercier (1) , Christophe Ritzenthaler (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We determine the structure of the graded ring of Siegel modular forms of degree 3. It is generated by 19 modular forms, among which we identify a homogeneous system of parameters with 7 forms of weights 4, 12, 12, 14, 18, 20 and 30. We also give a complete dictionary between the Dixmier-Ohno invariants of ternary quartics and the above generators.

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Reynald Lercier, Christophe Ritzenthaler. Siegel modular forms of degree three and invariants of ternary quartics. Proceedings of the American Mathematical Society, In press. ⟨hal-02186424⟩