Remarks on osculating linear spaces to projective varieties

yLet X subset of P-N be an integral n-dimensional variety and m(X, P, i) (resp. In(X, i)), 1 less than or equal to i less than or equal to N - n + 1, the Hermite invariants of X measuring the osculating behaviour of X at P (resp. at its general point). Here we prove m (X, x) + m (X, y) less than or equal to m (X, x+ y) and m (X, P, x) + m (X, y) less than or equal to m (X, P, x + y) for all integers x, y such that x + y < N - n + 1, the case n = 1 being known (M. Homma, A. Garcia and E. Esteves).