English

Siegel modular forms of degree three and invariants of ternary quartics

Number Theory 2024-05-16 v3 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1907.07431,
  title  = {Siegel modular forms of degree three and invariants of ternary quartics},
  author = {Reynald Lercier and Christophe Ritzenthaler},
  journal= {arXiv preprint arXiv:1907.07431},
  year   = {2024}
}