My question is how to explicitly compute the Chern class of the universal sheaf of the moduli space of ideal sheaves of two and three points on a given smooth projective variety X (no need to be algebraic surface) ? When we consider the two points case, the cohomology ring of the moduli can be explictly written down, I hope to represent the Chern class of the universal sheaf in terms of some element of cohomology ring of moduli and base manifold X.
