On the zero set of semi-invariants for tame quivers

Let d be a prehomogeneous dimension vector for a finitetame quiver Q. We show that the common zeros of allnon-constant semi-invariants for the variety of representationsof Q with dimension vector $Ncdotmathbf d$, under the product of the general linear groups at all vertices,is a complete intersection for $Ngeq 3$.