Siegel modular forms of degree three and invariants of ternary quartics

Lercier, Reynald; Ritzenthaler, Christophe

doi:10.1090/proc/14940

Siegel modular forms of degree three and invariants of ternary quartics
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by Reynald Lercier and Christophe Ritzenthaler

Proc. Amer. Math. Soc.

DOI: https://doi.org/10.1090/proc/14940

Published electronically: April 16, 2024

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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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