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December 2019 Multidimensional continued fractions for cyclic quotient singularities and Dedekind sums
Tadashi Ashikaga
Kyoto J. Math. 59(4): 993-1039 (December 2019). DOI: 10.1215/21562261-2019-0032

Abstract

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 3-dimensional Fourier–Dedekind sum in terms of our continued fraction.

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Tadashi Ashikaga. "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

Information

Received: 18 December 2015; Revised: 21 April 2017; Accepted: 23 June 2017; Published: December 2019
First available in Project Euclid: 10 August 2019

zbMATH: 07194003
MathSciNet: MR4032205
Digital Object Identifier: 10.1215/21562261-2019-0032

Subjects:
Primary: 11F20
Secondary: 11F23 , 14B05 , 14M25 , 32S45 , 57R18 , 58J20

Keywords: Continued fraction , cyclic quotient singularity , Dedekind sum , toric geometry

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 4 • December 2019
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