Graded rings of Hermitian modular forms with singularities

Abstract

We study graded rings of meromorphic Hermitian modular forms of degree two whose poles are supported on an arrangement of Heegner divisors. For the group SU2,2(O-K) where K is the imaginary-quadratic number field of discriminant -d, d is an element of {4, 7, 8, 11, 15, 19, 20, 24} we obtain a polynomial algebra without relations. In particular the Looijenga compactifications of the arrangement complements are weighted projective spaces.