Projective generation of ideals in polynomial extensions

Abstract

Let $R$ be an affine domain of dimension $n\ge 3$ over a field of characteristic $0$. Let $L$ be a projective $R\left[T\right]$-module of rank $1$ and $I\subset R\left[T\right]$ a local complete intersection ideal of height $n$. Assume that $I∕I^2$ is a surjective image of $L\oplus R{\left[T\right]}^{n-1}$. This paper examines under what conditions $I$ is a surjective image of a projective $R\left[T\right]$-module $P$ of rank $n$ with determinant $L$.