On the module of Zariski differentials and infinitesimal deformations of cusp singularities
type: Item
instance of: scholarly article
title: On the module of Zariski differentials and infinitesimal deformations of cusp singularities
zbMATH Open document ID: 0586.14002
DOI: 10.1007/BF01455802
author: Kurt Behnke
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163959
review text: The dimension of the space of first order infinitesimal deformations of a cusp singularity (X,0) is computed in terms of its resolution graph. One basic feature of the proof is to express this dimension in terms of 1- forms on the singularity (using local duality) and to analyze such 1- forms by expanding them as Fourier series on the universal cover of X- \(\{\) \(0\}\) (which is the neighbourhood of a cusp point in the product of two copies of the upper half plane with respect to a Hilbert modular group). A different proof of the result of this paper was given by \textit{I. Nakamura} [Math. Ann., to appear].
Mathematics Subject Classification ID: 14B07
Mathematics Subject Classification ID: 14B12
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14F10
zbMATH DE Number: 3939485
zbMATH Keywords: infinitesimal deformations
zbMATH Keywords: Zariski-differentials
zbMATH Keywords: dimension of the space of first order infinitesimal deformations of a cusp singularity
zbMATH Keywords: resolution graph
MaRDI profile type: Publication
cites work: Infinitesimal deformations of cusp singularities
cites work: Algebraische Eigenschaften der lokalen Ringe in den Spitzen der Hilbertschen Modulgruppen
cites work: Hilbert modular surfaces
cites work: Eigenschaften der lokalen Ringe in zweidimensionalen Spitzen
cites work: Rational surfaces with an anti-canonical cycle
cites work: Smoothings of normal surface singularities
OpenAlex ID: W2043724700
description: scientific article; zbMATH DE number 3939485