HOMOTOPY GROUPS OF CHOW VARIETIES

We show that a conjecture by Lawson holds, that is, the inclusion from the Chow variety C-p,C-d(P-n) of all effective algebraic p-cycles of degree d in n-dimensional projective space P-n to the space C-p(P-n) of effective algebraic p-cycles in P-n is 2d-connected. As a result, the homotopy and homology groups of C-p,C-d(P-n) are calculated up to 2d. We also obtain the homotopy groups up to a certain level for the space of algebraic cycles with a fixed degree.