Directed unions of local quadratic transforms of regular local rings and pullbacks

Abstract

Let $\{R_n,{\mathfrak{m}}_n{\}}_{n\ge 0}$ be an infinite sequence of regular local rings with $R_{n+1}$ birationally dominating $R_n$ and ${\mathfrak{m}}_n{R}_{n+1}$ a principal ideal of $R_{n+1}$ for each $n$. We examine properties of the integrally closed local domain $S={\bigcup }_{n\ge 0}{R}_n$.

23 pages; comments welcome