Abstract
M. Ishida and N. Iwashita classified three-dimensional canonical cyclic quotient singularities [11]. By using the classification, we shall discuss Hilbert basis resolutions via $\mathrm{Hilb}^{G}(\mathbb{C}^{3})$, Fujiki-Oka resolutions and iterated Fujiki-Oka resolutions. In particular, we shall prove that there exists a Hilbert basis resolution for any three-dimensional canonical cyclic quotient singularity.
Information
Published: 1 January 2023
First available in Project Euclid: 8 May 2023
Digital Object Identifier: 10.2969/aspm/08810209
Subjects:
Primary:
14B05
,
14J17
Secondary:
13H10
,
14J30
,
14L30
,
14M25
,
52B20
Keywords:
$G$-Hilbert schemes
,
canonical singularities
,
Dimension three
,
Fujiki-Oka resolutions
,
Hilbert basis resolutions
,
Iterated Fujiki-Oka resolutions
,
quotient singularities
,
toric varieties
Rights: Copyright © 2023 Mathematical Society of Japan
