AbstractWe study graded rings of meromorphic Hermitian modular forms of degree two whose poles are supported on an arrangement of Heegner divisors. For the group $$\mathrm {SU}_{2,2}({\mathcal {O}}_K)$$
SU
2
,
2
(
O
K
)
where K is the imaginary-quadratic number field of discriminant $$-d$$
-
d
, $$d \in \{4, 7,8,11,15,19,20,24\}$$
d
∈
{
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.