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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Zariski’s dimensionality type of singularities. Case of dimensionality type 2

Authors: Adam Parusiński and Laurenţiu Păunescu
Journal: J. Algebraic Geom.
Published electronically: November 2, 2022
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Abstract | References | Additional Information

Abstract: In the 1970s O. Zariski introduced a general theory of equisingularity for algebroid and algebraic hypersurfaces over an algebraically closed field of characteristic zero. His theory builds up on understanding the dimensionality type of hypersurface singularities, notion defined recursively by considering the discriminants loci of successive “generic” corank $1$ projections. The theory of singularities of dimensionality type 1, that is the ones appearing generically in codimension 1, was developed by Zariski in his foundational papers on equisingular families of plane curve singularities. In this paper we completely settle the case of dimensionality type 2, by studying Zariski equisingular families of surfaces singularities, not necessarily isolated, in the three-dimensional space.

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Additional Information

Adam Parusiński
Affiliation: Université Côte d’Azur, CNRS, LJAD, UMR 7351, 06108 Nice, France

Laurenţiu Păunescu
Affiliation: School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales, 2006, Australia
ORCID: 0000-0001-5796-276X

Received by editor(s): July 7, 2021
Received by editor(s) in revised form: May 16, 2022
Published electronically: November 2, 2022
Additional Notes: The first author is grateful for the support and hospitality of the Sydney Mathematical Research Institute (SMRI). This work was partially supported by ANR project LISA (ANR-17-CE40-0023-03).
Article copyright: © Copyright 2022 University Press, Inc.