On the Gauss Algebra Associated to a Rational Map d → n,

Letkbe a field of characteristic zero. Given a polynomial ringBoverkand a finitely generatedk-subalgebraA B, one associates toAak-subalgebra (A) Bin such a way that whenAis generated byn + 1 forms of the same degree then so is (A) and, moreover, in this case, (A) is the homogeneous coordinate ring of the Gauss image of Proj(A) nin the Plücker embedding of the Grassmannian (d, n), whered = dim Proj(A). The precise structure of (A) is established whenAis the homogeneous coordinate ring of a Veronese embedding of dor of a projective monomial curve.