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2021 Crepant Property of Fujiki-Oka Resolutions for Gorenstein Abelian Quotient Singularities
Kohei Sato, Yusuke Sato
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Nihonkai Math. J. 32(1): 41-69 (2021).

Abstract

We show a necessary and sufficient condition for the Fujiki-Oka resolutions of Gorenstein abelian quotient singularities to be crepant in all dimensions by using Ashikaga’s continued fractions. Moreover, we prove that any three dimensional Gorenstein abelian quotient singularity possesses a crepant Fujiki-Oka resolution as a corollary. This alternative proof of existence needs only simple computations compared with the results ever known.

Acknowledgments

We would like to thank Professor Tadashi Ashikaga for dedicated support, especially, helpful discussions at Tohokugakuin University. We also thank Professor Yukari Ito and Professor Alastair Craw for giving us many useful advices. National Institute of Technology, Oyama college has supported our study.

Citation

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Kohei Sato. Yusuke Sato. "Crepant Property of Fujiki-Oka Resolutions for Gorenstein Abelian Quotient Singularities." Nihonkai Math. J. 32 (1) 41 - 69, 2021.

Information

Received: 9 November 2020; Revised: 10 August 2021; Published: 2021
First available in Project Euclid: 3 May 2022

Subjects:
Primary: 14B05 , 14J17
Secondary: 13H10 , 14C17 , 14J30 , 14J35 , 14J40 , 14L30 , 14M25 , 52B20

Keywords: Abelian groups , Crepant resolutions , finite groups , Fujiki-Oka resolutions , Higher dimension , Hirzebruch-Jung continued fractions , invariant theory , multidimensional continued fractions , quotient singularities , toric varieties

Rights: Copyright © 2021 Niigata University, Department of Mathematics

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Vol.32 • No. 1 • 2021
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