On Gorenstein surface singularities with fundamental genus \(p_ f\geq 2\) which satisfy some minimality conditions
type: Item
instance of: scholarly article
title: On Gorenstein surface singularities with fundamental genus \(p_ f\geq 2\) which satisfy some minimality conditions
zbMATH Open document ID: 0848.14017
author: Tadashi Tomaru
published in: Pacific Journal of Mathematics
publication date: 1996-08-29T00:00:00Z
review text: In this paper we study normal surface singularities whose fundamental genus (:= the arithmetic genus \(p_a (Z)\) of the fundamental cycle \(Z)\) is equal or greater than 2. For those singularities, we define some minimality conditions which are similar to Laufer's conditions for elliptic singularities, and we study the relation between them under the condition to be Gorenstein. Especially, we prove that ``If \(\pi : (\widetilde X,A) \to (X,x)\) is a resolution of a Gorenstein surface singularity with \(p_g (X,x) \geq 1\) and \(K = Z + E\), then \(p_g (X,x) = p_a (Z) + 1\), where \(K\) and \(E\) are the canonical cycle and minimal cycle, respectively''. Further we define some sequence of such singularities, which is analogous to elliptic sequence in the sense of Yau. In the case of hypersurface singularities of Brieskorn type, we study some properties of the sequences.
reviewed by: Tadashi Tomaru
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 14E15
zbMATH DE Number: 910229
zbMATH Keywords: normal surface singularities
zbMATH Keywords: fundamental genus
zbMATH Keywords: resolution
zbMATH Keywords: Gorenstein surface
zbMATH Keywords: hypersurface singularities
MaRDI profile type: Publication
full work available at URL: pjm.1995.170.271
OpenAlex ID: W1593730012
DOI: 10.2140/PJM.1995.170.271
description: scientific article; zbMATH DE number 910229