The Hodge-Deligne polynomials of some moduli spaces of coherent systems

After proving the existence of (non-split, non-degenerate) universal families of extensions of coherent systems (in the spirit of Lange). we are able to describe wallcrossing for some moduli spaces of coherent systems. This allows us to compute the Hodge-Deligne polynomials of the moduli spaces of coherent systems of type (1,d,n) for n=2,3 and of type (2,d,2) for d odd big enough