Projective spaces as orthogonal modular varieties

Abstract

We construct $16$ reflection groups $\Gamma$ 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 $\mathcal{D}/\Gamma$ 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.

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Cited by in corpus (2)

• Congruence Subgroups and Orthogonal Groups
• Simple lattices and free algebras of modular forms