Siegel modular forms of degree three and invariants of ternary quartics - Archive ouverte HAL
Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2021

Siegel modular forms of degree three and invariants of ternary quartics

Résumé

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.
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Commentaire The full list of expressions for the Siegel modular forms either in terms of the theta constants or in terms of curve invariants, the expressions of curve invariants in terms of Siegel modular forms and the relations in the algebra.
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Dates et versions

hal-02186424 , version 1 (18-07-2019)

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Reynald Lercier, Christophe Ritzenthaler. Siegel modular forms of degree three and invariants of ternary quartics. Proceedings of the American Mathematical Society, In press, ⟨10.1090/proc/14940⟩. ⟨hal-02186424⟩
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