On the zero set of semi-invariants for tame quivers

Abstract

Let $\mathbf{d}$ be a prehomogeneous dimension vector for a finite tame quiver $Q$. We show that the common zeros of all non-constant semi-invariants for the variety of representations of $Q$ with dimension vector $N\cdot \mathbf{d}$, under the product of the general linear groups at all vertices, is a complete intersection for $N\ge 3$.