Siegel modular forms of degree three and invariants of ternary quartics

Reynald Lercier; Christophe Ritzenthaler

doi:10.1090/proc/14940

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arXiv · 1907.07431

Siegel modular forms of degree three and invariants of ternary quartics

Reynald Lercier·Christophe Ritzenthaler

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Abstract

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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Reynald Lercier, Christophe Ritzenthaler. 2019-07-17. Siegel modular forms of degree three and invariants of ternary quartics. https://doi.org/10.1090/proc/14940

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