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Let $(R, \mathfrak{m})$ be a regular local ring of dimension $d \geq 2$. A local monoidal transform of $R$ is a ring of the form $R_1= R[\frac{\mathfrak{p}}{x}]_{\mathfrak{m}_1}$ where $x \in \mathfrak{p}$ is a regular parameter, $\mathfrak{p}$ is a regular prime ideal of $R$ and $ \mathfrak{m}_1 $ is a maximal ideal of $ R[\frac{\mathfrak{p}}{x}] $ lying over $ \mathfrak{m}. $ In this article we study some features of the rings $ S= \cup_{n \geq 0}^{\infty} R_n $ obtained as infinite directed union of iterated local monoidal transforms of $R$. In order to study when these rings are GCD domains, we also provide results in the more general setting of directed unions of GCD domains.

Directed unions of local monoidal transforms and GCD domains