Counting divisorial contractions with centre a $c{A}_n$-singularity

Abstract

First, we simplify the existing classification due to Kawakita and Yamamoto of 3-dimensional divisorial contractions with centre a $c{A}_n$-singularity, also called 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 $c{A}_n$-singularity. We show that if there exists one such divisorial contraction, then there exist uncountably many such divisorial contractions.

18 pages, to appear in Publications of the Research Institute for Mathematical Sciences, Kyoto University. Update the theorem numbering of the citation [Pae21]