Characterization of currents associated with algebraic cycles by their chow transform

Our main result is the characterization of the divisors of the Grassmannian G(q-1,n) which are Chow transforms of (q, q)-currents on P-n. This allows us to characterize the currents associated to algebraic cycles as being those whose direct image by a Veronese embedding has a divisor as Chow transform. The ingredients of the proof are on the one hand a characterization of Chow forms as solutions of a system of differential equations that we obtain by a direct method. On the other hand we use classical results of integral geometry which express the image of the Chow transformation as the space of solutions of a system of ultra-hyperbolic equations a priori of order 2q + 2 that we then succeed in reducing. (C) 2000 Editions scientifiques et medicales Elsevier SAS.