On the Gauss algebra associated to a rational map P-d -> P-n

Let k be a field of characteristic zero. Given a polynomial ring B over k and a finitely generated k-subalgebra A subset of B, one associates to A a k-subalgebra G(A) subset of B in such a way that when A is generated by n + 1 forms of the same degree then so is G(A) and, moreover, in this case, G(A) is the homogeneous coordinate ring of the Gauss image of Proj(A) subset of P-n in the Plucker embedding of the Grassmannian G(d, n), where d = dim Proj(A). The precise structure of G(A) is established when A is the homogeneous coordinate ring of a Veronese embedding of P-d Or Of a projective monomial curve. (C) 1998 Academic Press.207255757