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December 2019 Canonical singularities of dimension three in characteristic 2 which do not follow Reid’s rules
Masayuki Hirokado
Kyoto J. Math. 59(4): 747-768 (December 2019). DOI: 10.1215/21562261-2019-0026

Abstract

We continue studying compound Du Val singularities defined over an algebraically closed field k, and present concrete examples in characteristic 2 which have one-dimensional singular loci but do not admit a description as a trivial product (a rational double point) × (a curve) up to analytic isomorphism at any point. Unlike in other characteristics, we find a large number of such examples whose general hyperplane sections have rational double points of type D. These compound Du Val singularities shall be viewed as a special class of canonical singularities. In the previous work with Ito and Saito, we classified such singularities in p3,

and I intend to complete our classification in arbitrary characteristic, reinforcing Reid’s result in characteristic 0.

Citation

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Masayuki Hirokado. "Canonical singularities of dimension three in characteristic 2 which do not follow Reid’s rules." Kyoto J. Math. 59 (4) 747 - 768, December 2019. https://doi.org/10.1215/21562261-2019-0026

Information

Received: 4 April 2016; Revised: 22 May 2017; Accepted: 29 May 2017; Published: December 2019
First available in Project Euclid: 17 July 2019

zbMATH: 07193996
MathSciNet: MR4032198
Digital Object Identifier: 10.1215/21562261-2019-0026

Subjects:
Primary: 14B05
Secondary: 14B07, 14G17, 14J17

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 4 • December 2019
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