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Newton–Okounkov Bodies of Exceptional Curve Plane Valuations Non-positive at Infinity

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Extended Abstracts February 2016

Part of the book series: Trends in Mathematics ((RPCRMB,volume 9))

Abstract

In this note we announce a result determining the Newton–Okounkov bodies of the line bundle \(\mathcal {O}_{\mathbb {P}^2} (1)\) with respect to exceptional curve plane valuations non-positive at infinity.

The authors wish to thank J. Roé and A. Küronya for stimulating their interest in Newton–Okounkov bodies as well as for their helpful comments and for pointing out a more customary name for our valuations. The first three authors were partially supported by the Spanish Government Ministerio de Economía y Competitividad (MINECO), grants MTM2012-36917-C03-03 and MTM2015-65764-C3-2-P, as well as by Universitat Jaume I, grant P1-1B2015-02.

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Author information

Authors and Affiliations

  1. Departament de Matemàtiques, Institut Universitari de Matemàtiques i Aplicacions de Castelló, Universitat Jaume I, Campus de Riu Sec, 12071, Castellón de la Plana, Spain

    Carlos Galindo & Julio José Moyano-Fernández

  2. Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022, València, Spain

    Francisco Monserrat

  3. FB Informatik und Mathematik, Goethe-Universität Frankfurt, 60054, Frankfurt am Main, Germany

    Matthias Nickel

Authors
  1. Carlos Galindo
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  2. Francisco Monserrat
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  3. Julio José Moyano-Fernández
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  4. Matthias Nickel
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Corresponding author

Correspondence to Carlos Galindo .

Editor information

Editors and Affiliations

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

    Maria Alberich-Carramiñana

  2. Departament de Matemàtiques, University Jaume I, Castellón, Spain

    Carlos Galindo

  3. Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt, Germany

    Alex Küronya

  4. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain

    Joaquim Roé

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Galindo, C., Monserrat, F., Moyano-Fernández, J.J., Nickel, M. (2018). Newton–Okounkov Bodies of Exceptional Curve Plane Valuations Non-positive at Infinity. In: Alberich-Carramiñana, M., Galindo, C., Küronya, A., Roé, J. (eds) Extended Abstracts February 2016. Trends in Mathematics(), vol 9. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-00027-1_1

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