Moduli of representations of one-point extensions

We study moduli spaces of (semi-)stable representations of one-point extensions of quivers by rigid representations. This class of moduli spaces unifies Grassmannians of subrepresentations of rigid representations and moduli spaces of representations of generalized Kronecker quivers. With homological methods, we find numerical criteria for non-emptiness and results on basic geometric properties, construct generating semi-invariants, expand the Gel'fand MacPherson correspondence, and derive a formula for the Poincaré polynomial in singular cohomology of these moduli spaces.