 Holomorphic volume form

On a complex manifold of complex dimension $n$, a holomorphic volume form is a nowhere-vanishing holomorphic differential form of type $(n,0)$. On ${\mathbb{C}}^n$, the form $d{z}_1\wedge \cdots \wedge d{z}_n$ transforms under a complex linear coordinate change by the determinant. It is consequently preserved by the special unitary group $SU(n)$.