Some Betti numbers of the moduli of 1-dimensional sheaves on P2

Let M(d,chi), with (d, chi) = 1, be the moduli space of semistable sheaves on P-2 supported on curves of degree d and with Euler characteristic chi. The cohomology ring H*(M(d, chi), Z) of M(d, chi.) is isomorphic to its Chow ring A*(M(d, chi)) by Markman's result. Pi and Shen have described a minimal generating set of A*(M(d, chi)) consisting of 3d - 7 generators, which they also showed to have no relation in A(<= d-2)(M(d, chi)). We compute the two Betti numbers b(2(d-1)) and b(2d) of M(d, chi), and as a corollary we show that the generators given by Pi and Shen have no relations in A(<= d-1)(M(d, chi)), but do have three linearly independent relations in A(d)(M(d, chi)).