Quivers of type Dn, semi-invariants and complete intersections

Let Q be a quiver of type Dn and d a sincere dimension vector for Q. We give a necessary and sufficient condition for the set of common zeros of all non-constant semi-invariants for d-dimensional representations of Q, under the product of the general linear groups at all vertices of Q, to be a set theoretical complete intersection. Up to now, only sufficient conditions were known.