Rational equivalence on some families of plane curves
Ann. Inst. Fourier (Grenoble) 44 (1994), no. 2, 323--345.

AIF paper page.

Abstract. If V_d,δ denotes the variety of irreducible plane curves of degree d with exactly δ nodes as singularities, Diaz and Harris (1986) have conjectured that Pic(V_d,δ) is a torsion group. In this note we study rational equivalence on some families of singular plane curves and we prove, in particular, that Pic(V_d,1) is a finite group, so that the conjecture holds for δ = 1. Actually the order of Pic(V_d,1) is 6(d-2)(d² -3d+1), the group being cyclic if d is odd and the product of Z₂ and a cyclic group of order 3(d-2)(d² -3d+1) if d is even.