Simple lattices and free algebras of modular forms

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 $3\le n\le 10$, 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.

arXiv comment37 pages

References in corpus (6)

• Structure of the module of vector-valued modular forms
• Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections
• On some free algebras of orthogonal modular forms
• The classification of free algebras of orthogonal modular forms
• The ring of modular forms for the even unimodular lattice of signature (2,10)
• Projective spaces as orthogonal modular varieties

Cited by in corpus (2)

• Free algebras of modular forms on ball quotients
• Maximal Discrete Subgroups of $S{O}^{+}(2,n+2)$