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 ${\mathfrak m}nR{n+1}$ a principal ideal of $R_{n+1}$ for each $n$. We examine properties of the integrally closed local domain $S = \bigcup_{n \ge 0}R_n$.