Breve descrizione dei contenuti: Let X1,...,Xs be integral subvariety of an ambient projective space. Fix positive integers k1,...,ks,t. Let J(t) be the closure of the set of
all t-dimensional linear subspaces of a linear space spanned by k1 points of X1,...,ks points of Xs. Here we prove that J(t) has the expected dimension if each Xi is a surface and either s=3,k1=k2=k3=t=1 or s=2,k1=2,k2=t=1.