Hilbert desingularizations for three dimensional canonical cyclic quotient singularities

Kohei Sato; Yusuke Sato

Hilbert desingularizations for three dimensional canonical cyclic quotient singularities

Algebraic Geometry 2021-08-06 v1

Authors: Kohei Sato , Yusuke Sato

Abstract

In this paper, we shall discuss Hilbert property of ${\rm Hilb}^{G}(\mathbb{C}^{3})$ , Fujiki-Oka resolutions and iterated Fujiki-Oka resolutions for three dimensional canonical cyclic quotient singularities by using the classification shown by Ishida and Iwashita\cite{II}. Finally, we shall prove that there exists a Hilbert desingularization for any three dimensional canonical cyclic quotient singularity.

Keywords

hilbert functions singularity theory

Cite

@article{arxiv.2108.02402,
  title  = {Hilbert desingularizations for three dimensional canonical cyclic quotient singularities},
  author = {Kohei Sato and Yusuke Sato},
  journal= {arXiv preprint arXiv:2108.02402},
  year   = {2021}
}

Comments

11 pages, 3 figures

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