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Siegel modular forms of degree three and invariants of ternary quartics

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arxiv 1907.07431 v3 pith:H4IJBMBX submitted 2019-07-17 math.NT math.AG

Reynald Lercier , Christophe Ritzenthaler This is my paper · ORCID
classification math.NTmath.AG
keywords formsmodulardegreeinvariantsquarticssiegelternaryabove
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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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  1. Concomitants of Ternary Quartics and Vector-valued Siegel and Teichm\"uller Modular Forms of Genus Three

    math.AG 2019-08 conditional novelty 7.0 of 10

    Concomitants of ternary quartics parametrize all vector-valued Siegel modular forms of degree 3, with boundary vanishing orders matched to double-conic vanishing orders.

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