Generating Picard modular forms by means of invariant theory

Fabien Cléry; Gerard van der Geer

Generating Picard modular forms by means of invariant theory

Algebraic Geometry 2022-03-01 v2

Authors: Fabien Cléry , Gerard van der Geer

Abstract

We use the description of the Picard modular surface for discriminant $-3$ as a moduli space of curves of genus $3$ to generate all vector-valued Picard modular forms from bi-covariants for the action of ${GL}_2$ on the space of pairs of binary forms of bidegree $(4,1)$ . The universal binary forms of degree $4$ and $1$ correspond to a meromorphic modular form of weight $(4,-2)$ and a holomorphic Eisenstein series of weight $(1,1)$ .

Keywords

picard modular forms invariant theory moduli space binary forms eisenstein series picard modular surface

Cite

@article{arxiv.2110.00849,
  title  = {Generating Picard modular forms by means of invariant theory},
  author = {Fabien Cléry and Gerard van der Geer},
  journal= {arXiv preprint arXiv:2110.00849},
  year   = {2022}
}

Comments

41 pages; minor changes. To appear in PAMQ

Generating Picard modular forms by means of invariant theory

Abstract

Keywords

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