2020/09/28 by Haowu Wang, Brandon Williams, Wang, Haowu +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2009.13343
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≤ n ≤ 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.