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Two Points of the Boundary of Toric Geometry

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Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Abstract

This note presents two observations which have in common that they lie at the boundary of toric geometry. The first one because it concerns the deformation of affine toric varieties into non toric germs in order to understand how to avoid some ramification problems arising in the study of local uniformization in positive characteristic, and the second one because it uses limits of projective systems of equivariant birational maps of toric varieties to study the space of additive preorders on Z r for r ≥ 2.

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Notes

  1. 1.

    The Hamburger-Noether expansion is an algorithm extracting in any characteristic a description of the resolution process by point blowing-ups from a parametric representation x(t), y(t).

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Acknowledgements

I am grateful to Hussein Mourtada for interesting discussions of the first topic of this note and for calling my attention to the phenomenon described in the case p = 2.

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Authors and Affiliations

  1. CNRS, Institut Mathématique de Jussieu-Paris Rive Gauche, Paris, France

    Bernard Teissier

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  1. Bernard Teissier
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Correspondence to Bernard Teissier .

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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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Teissier, B. (2018). Two Points of the Boundary of Toric Geometry. 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_4

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