Title:An observation on the Poincaré polynomials of moduli spaces of one-dimensional sheaves

Abstract:We notice that for $0<d\le 6$ the Poincaré polynomial of Simpson moduli space $M_{dm + 1}(\mathbb P_2)$ is divisible by the Poincaré polynomial of the projective space $\mathbb P_{3d-1}$. A somehow regular behaviour of the difference of the Poincaré polynomials of the Hilbert scheme of $\frac{(d-2)(d-1)}{2}$ points on $\mathbb P_2$ and the moduli space of Kronecker modules $N(3; d-2, d-1)$ is noticed for $d=4, 5, 6$.