  We investigate the geometry of the Simpson moduli space M of stable sheaves
on P_3 with Hilbert polynomial H(m)=3m+1 and describe explicitly the two
smooth, rational components, their 11-dimensional smooth, transversal
intersection and the relation between M and the Hilbert scheme Hilb_H(P_3) of
cubic space curves. We also compute the Betti numbers of the Chow groups of the
moduli space M.
