Moduli spaces of framed sheaves and quiver varieties

The second part is devoted to a detailed study of framed sheaves on the Hirzebruch surface Σn in the case when the invariant expressing the necessary and sufficient condition for the nonemptiness of moduli spaces attains its minimum (what we call the “minimal case”). Our main result is that, under this assumption, the corresponding moduli space is isomorphic to a Grassmannian (when n=1), or to the direct sum of n−1 copies of the cotangent bundle of a Grassmannian (when n≥2). Finally, by slightly generalizing a construction due to Nakajima, we prove that these moduli spaces admit a description as quiver varieties.