On the zero set of semi-invariants for regular modules over tame canonical algebras. (Q2477648)

With a finite dimensional basic algebra and a dimension vector one associates the variety of modules of the given dimension vector. The base change group acts on this affine variety, and a polynomial function on the module variety is a semi-invariant if it spans an invariant subspace with respect to the group action. The main result of the paper is that for a tame canonical algebra and a regular dimension vector (sufficiently large in a sense made precise in the paper), the common zero locus in the associated module variety of the non-constant semi-invariants is a complete intersection. As a corollary, the coordinate ring of the module variety is a free module over the algebra of semi-invariants. Analogous results were known before for representation spaces of quivers. The present work seems to be the first examining quivers with relations from this point of view.