Deformations of three dimensional cusp singularities
type: Item
instance of: scholarly article
title: Deformations of three dimensional cusp singularities
zbMATH Open document ID: 0678.14001
author: Hiroyasu Tsuchihashi
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1986-01-01T00:00:00Z
review text: The author continues his investigation of cusp singularities [ibid. 35, 607-639 (1983; Zbl 0585.14004)]. This time he studies deformations of 3- dimensional cusp singularities (V,p), which are not of Hilbert modular type. [The Hilbert modular cusp singularities in dimension 3 or more are rigid, see \textit{E. Freitag} and \textit{R. Kiehl}, Invent. Math. 24, 121-148 (1974; Zbl 0304.32018).] Using toric variety techniques, the author constructs an open cover of the exceptional (toric) divisor of a resolution of (V,p). Using this, a deformation of the resolution is obtained, which contracts to a deformation of (V,p). This family is actually the versal family, proving that these cusp singularities are unobstructed and non-smoothable. A preceding group cohomology computation implies that they are not taut.
Mathematics Subject Classification ID: 14B07
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 4110825
zbMATH Keywords: deformations of 3-dimensional cusp singularities
zbMATH Keywords: toric variety
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228451
OpenAlex ID: W1977327222
cites work: Algebraische Eigenschaften der lokalen Ringe in den Spitzen der Hilbertschen Modulgruppen
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cites work: Q4726370
DOI: 10.2748/TMJ/1178228451
description: scientific article; zbMATH DE number 4110825