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Simple lattices and free algebras of modular forms

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Title
Simple lattices and free algebras of modular forms
Author(s)
Haowu Wang; Williams, Brandon
Publication Date
2023-01
Journal
Advances in Mathematics, v.413
Publisher
Academic Press
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≤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. © 2022 Elsevier Inc.
URI
https://pr.ibs.re.kr/handle/8788114/12448
DOI
10.1016/j.aim.2022.108835
ISSN
0001-8708
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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