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Singularities in Positive Characteristic: Equisingularity, Classification, Determinacy

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Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

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Abstract

In this survey paper we give an overview on some aspects of singularities of algebraic varieties over an algebraically closed field of arbitrary characteristic. We review in particular results on equisingularity of plane curve singularities, classification of hypersurface singularities and determinacy of arbitrary singularities. The section on equisingularity has its roots in two important early papers by Antonio Campillo. One emphasis is on the differences between positive and zero characteristic and on open problems.

Dedicated to Antonio Campillo on the occasion of his 65th birthday

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References

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Kaiserslautern, Kaiserslautern, Germany

    Gert-Martin Greuel

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  1. Gert-Martin Greuel
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Correspondence to Gert-Martin Greuel .

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Editors and Affiliations

  1. Fachbereich Mathematik, Universität Kaiserslautern, Kaiserslautern, Germany

    Gert-Martin Greuel

  2. Departamento de Álgebra, Instituto de Matemáticas (IMUS), Universidad de Sevilla, Sevilla, Spain

    Luis Narváez Macarro

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Sebastià Xambó-Descamps

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Greuel, GM. (2018). Singularities in Positive Characteristic: Equisingularity, Classification, Determinacy. In: Greuel, GM., Narváez Macarro, L., Xambó-Descamps, S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, Cham. https://doi.org/10.1007/978-3-319-96827-8_2

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