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An Introduction to Resolution of Singularities via the Multiplicity

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Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Abstract

In these notes we study properties of the multiplicity at points of a variety X over a perfect field. We focus on properties that can be studied using ramification method, such as discriminants and some generalized discriminants that we shall introduce. We also show how these methods lead to an alternative proof of resolution of singularities for varieties over fields of characteristic zero.

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Authors and Affiliations

  1. CIEM-FAMAF, Universidad Nacional de Córdoba, Córdoba, Argentina

    Diego Sulca

  2. ICMAT-Universidad Autónoma de Madrid, Madrid, Spain

    Orlando Villamayor U.

Authors
  1. Diego Sulca
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  2. Orlando Villamayor U.
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Corresponding author

Correspondence to Orlando Villamayor U. .

Editor information

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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Sulca, D., Villamayor U., O. (2018). An Introduction to Resolution of Singularities via the Multiplicity. 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_11

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