On the zero set of semi-invariants for Dn-quivers

Let Q be a quiver of type Dn, d a dimension vector for Q, and T a representative of the open orbit of the variety rep(Q,d) of d-dimensional representations of Q, under the product Gl(d) of the general linear groups at all vertices of Q. Let be a decomposition of T into pairwise non-isomorphic indecomposable representations Ti with multiplicities λi. We show that it depends on the multiplicity of at most one such direct summand whether or not the set of common zeros of all non-constant semi-invariants for rep(Q,d), with respect to the action of Gl(d), is a set theoretical complete intersection.