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Superisolated Surface Singularities

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Artal Bartolo, Enrique and Luengo Velasco, Ignacio and Melle Hernández, Alejandro (2006) Superisolated Surface Singularities. In Singularities and computer algebra. London Mathematical Society Lecture Note Series (324). Cambridge University Press, Cambridge, pp. 13-39. ISBN 9780521683098

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Official URL: http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511526374&cid=CBO9780511526374A015



Abstract

In this survey, we review part of the theory of superisolated surface singularities (SIS) and its applications including some new and recent developments. The class of SIS singularities is, in some sense, the simplest class of germs of normal surface singularities. Namely, their tangent cones are reduced curves and the geometry and topology of the SIS singularities can be deduced from them. Thus this class contains, in a canonical way, all the complex projective plane curve theory, which gives a series of nice examples and counterexamples. They were introduced by I. Luengo to show the non-smoothness of the μ-constant stratum and have been used to answer negatively some other interesting open questions. We review them and the new results on normal surface singularities whose link are rational homology spheres. We also discuss some positive results which have been proved for SIS singularities


Item Type:Book Section
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Papers from the conference held at the University of Kaiserslautern, Kaiserslautern, October 18–20, 2004

Uncontrolled Keywords:normal surface singularities, plane curves, monodromy, deformations
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:20961
Deposited On:19 Apr 2013 16:44
Last Modified:02 Aug 2018 11:48

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