ML invariant of the symmetric algebra of a projective module over a one dimensional affine domain

Let k be an algebraically closed field and let A be an affine domain of dimension one over k. Let P be a finitely generated projective A-module of rank d and let R=SymA(P) be the symmetric algebra of P over A. Assume that A is not a polynomial algebra over k. In this article we show that, under these assumptions, the Makar-Limanov invariant ML(R)=A.