论文标题
射影空间作为正交模块化品种
Projective spaces as orthogonal modular varieties
论文作者
论文摘要
We construct $16$ reflection groups $Γ$ acting on symmetric domains $\mathcal{D}$ of Cartan type IV, for which the graded algebras of modular forms are freely generated by forms of the same weight, and in particular the Satake--Baily--Borel compactification of $\mathcal{D} / Γ$ is isomorphic to a projective space.其中有四个是Freitag-Salvati Manni，Matsumoto，Perna和Runge的已知结果。此外，我们发现了几个新型的正交类型的模块化组，它们的模块化形式的代数是自由生成的。
We construct $16$ reflection groups $Γ$ acting on symmetric domains $\mathcal{D}$ of Cartan type IV, for which the graded algebras of modular forms are freely generated by forms of the same weight, and in particular the Satake--Baily--Borel compactification of $\mathcal{D} / Γ$ is isomorphic to a projective space. Four of these are previously known results of Freitag--Salvati Manni, Matsumoto, Perna and Runge. In addition we find several new modular groups of orthogonal type whose algebras of modular forms are freely generated.
