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PreprintCC BY 4.0arXiv

Tautological modular forms of level two and degree two

  • Fabien Cléry
  • Gerard van der Geer
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Abstract

We show how to use divisors on the projectivized Hodge bundle to construct special vector-valued modular forms and then apply invariant theory to construct all vector-valued Siegel modular forms of level two and degree two. Thus we construct all modular forms in terms of certain basic modular forms that are intimately connected to the moduli of curves of genus two.

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Cite

BibTeXRIS
BibTeX
@misc{clery2026tautological,
  title = {{Tautological modular forms of level two and degree two}},
  author = {Fabien Cléry and Gerard van der Geer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.13300},
  eprint = {2605.13300},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.13300},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Tautological modular forms of level two and degree two
AU  - Fabien Cléry
AU  - Gerard van der Geer
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2605.13300
UR  - https://arxiv.org/abs/2605.13300
AB  - We show how to use divisors on the projectivized Hodge bundle to construct special vector-valued modular forms and then apply invariant theory to construct all vector-valued Siegel modular forms of level two and degree two. Thus we construct all modular forms in terms of certain basic modular forms that are intimately connected to the moduli of curves of genus two.
ER  -