Counting Divisorial Contractions with Centre a $cA_{n}$-Singularity

First, we simplify the existing classification due to Kawakita and Yamamoto of 3 -dimensional divisorial contractions with centre a cA_{n} -singularity, also called a compound A_{n} singularity. Next, we describe the global algebraic divisorial contractions corresponding to a given local analytic equivalence class of divisorial contractions with centre a point. Finally, we consider divisorial contractions of discrepancy at least 2 to a fixed variety with centre a cA_{n} -singularity. We show that if there exists one such divisorial contraction, then there exist uncountably many such divisorial contractions.