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arXiv · 2009.13343

Simple lattices and free algebras of modular forms

Haowu Wang·Brandon Williams
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Abstract

We study the algebras of modular forms on type IV symmetric domains for simple lattices; that is, lattices for which every Heegner divisor occurs as the divisor of a Borcherds product. For every simple lattice $L$ of signature $(n,2)$ with $3\leq n \leq 10$, we prove that the graded algebra of modular forms for the maximal reflection subgroup of the orthogonal group of $L$ is freely generated. We also show that, with five exceptions, the graded algebra of modular forms for the maximal reflection subgroup of the discriminant kernel of $L$ is also freely generated.

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Haowu Wang, Brandon Williams. 2020-09-28. Simple lattices and free algebras of modular forms. https://arxiv.org/abs/2009.13343

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