We present a multidimensional continued fraction of Hirzebruch–Jung type which controls a certain resolution of an isolated cyclic quotient singularity, and we study its geometric properties. As an application, we explicitly express a certain -dimensional Fourier–Dedekind sum in terms of our continued fraction.
"Multidimensional continued fractions for cyclic quotient singularities and Dedekind sums." Kyoto J. Math. 59 (4) 993 - 1039, December 2019. https://doi.org/10.1215/21562261-2019-0032