论文标题
简单的晶格和模块化形式的自由代数
Simple lattices and free algebras of modular forms
论文作者
论文摘要
我们研究了简单晶格的IV型对称结构域上模块化形式的代数。也就是说，每个Heegner Divisor都作为Borcherds产品的除数出现的格子。对于每个简单的晶格$ l $ signature $（n，2）$带有$ 3 \ leq n \ leq 10 $，我们证明，$ l $的正交组的最大反射子组的模块化形式的分级代数是自由产生的。我们还表明，除了五个例外，还可以自由生成$ l $的判别核的最大反射子组的模块化形式的分级代数。
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.
