IRREDUCIBLE COMPONENTS OF QUIVER GRASSMANNIANS

We consider the action of a smooth, connected group scheme G on a scheme Y, and discuss the problem of when the saturation map Theta: G x X -> Y is separable, where X subset of Y is an irreducible subscheme. We provide sufficient conditions for this in terms of the induced map on the fibres of the conormal bundles to the orbits. Using jet space calculations, one then obtains a criterion for when the scheme-theoretic image of Theta is an irreducible component of Y. We apply this result to Grassmannians of submodules and several other schemes arising from representations of algebras, thus obtaining a decomposition theorem for their irreducible components in the spirit of the result by Crawley-Boevey and Schroer for module varieties.