The second pluri-genus of smoothable Gorenstein surface singularities
type: Item
instance of: scholarly article
title: The second pluri-genus of smoothable Gorenstein surface singularities
zbMATH Open document ID: 1194.32013
author: Rong Du
author: Stephen Yau
published in: Science China. Mathematics
publication date: 2010-05-26T00:00:00Z
review text: Let \((X,x)\) be a Gorenstein smoothable singularity with \(p_g(X,x)\geq 1\). It is proved that \[ \delta_2(X,x)=h^1(S)+\mu(X,x)-\tau(X,x)-p_g(X,x)+1\;. \] Here \(\mu(X,x)\) and \(\tau(X,x)\) are the generalized Milnor number and Tjurina number of \((X,x), \delta_2(X,x)\) is the second pluri-genus and \(p_g(X,x)\) the geometric genus. \(f:(M, E)\to (X,x)\) is the minimal good resolution, \(E\) the exceptional divisor, and \(S=(\Omega_M^1(\log E))^\ast\). This is a generalization of the corresponding result of Okuma, for complete intersection isolated surface singularities.
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 32S10
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 32S30
Mathematics Subject Classification ID: 32S45
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14B07
zbMATH DE Number: 5712123
zbMATH Keywords: second pluri-genus
zbMATH Keywords: smoothable
zbMATH Keywords: Gorenstein
zbMATH Keywords: Milnor number
zbMATH Keywords: Tjurina number
MaRDI profile type: Publication
full work available at URL: s11425-010-0062-2
OpenAlex ID: W1989266106
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DOI: 10.1007/S11425-010-0062-2
description: scientific article; zbMATH DE number 5712123