Some free algebras of automorphic forms on symmetric domains of type IV

摘要

Some arithmetic quotients of symmetric domains of type IV can be interpreted as moduli varieties of multipolarized K3 surfaces. Making use of this interpretation, we prove that, for n = 3, 4, 5, 6, 7, some natural algebras of automorphic forms on the n-dimensional symmetric domains of type IV are free, and we find the degrees of their generators. This implies that the corresponding arithmetic groups are generated by complex reflections.