Homogeneous affine surfaces: Moduli spaces

We analyze the moduli space of non-flat homogeneous affine connections on surfaces. For Type AA surfaces, we write down complete sets of invariants that determine the local isomorphism type depending on the rank of the Ricci tensor and examine the structure of the associated moduli space. For Type BB surfaces which are not Type AA we show the corresponding moduli space is a simply connected real analytic 4-dimensional manifold with second Betti number equal to 1.