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  • Conference proceedings
  • © 2018

Extended Abstracts February 2016

Positivity and Valuations

Birkhäuser
  • Presents new results of active areas in algebraic geometry

  • Covers a wide range of topics

  • Includes open problems

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

Part of the book sub series: Research Perspectives CRM Barcelona (RPCRMB)

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  • ISBN: 978-3-030-00027-1
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Table of contents (18 papers)

  1. Front Matter

    Pages i-x
  2. Newton–Okounkov Bodies of Exceptional Curve Plane Valuations Non-positive at Infinity

    • Carlos Galindo, Francisco Monserrat, Julio José Moyano-Fernández, Matthias Nickel
    Pages 1-7
  3. Non-positive at Infinity Valuations

    • Francisco Monserrat
    Pages 27-32
  4. Computing Multiplier Ideals in Smooth Surfaces

    • Guillem Blanco, Ferran Dachs Cadefau
    Pages 57-63
  5. On the Containment Hierarchy for Simplicial Ideals

    • Magdalena Lampa-Baczyńska, Grzegorz Malara
    Pages 71-74
  6. Algebraic Volumes of Divisors

    • Carsten Bornträger, Matthias Nickel
    Pages 83-87
  7. Duality on Value Semigroups

    • Laura Tozzo
    Pages 99-104
  8. Notes on Local Positivity and Newton–Okounkov Bodies

    • Harold Blum, Grzegorz Malara, Georg Merz, Justyna Szpond
    Pages 105-111
  9. Newton–Okounkov Bodies and Reified Valuations of Higher Rank

    • Alberto Camara, Iago Giné, Roberto Gualdi, Nikita Kalinin, Joaquim Roé, Martin Ulirsch et al.
    Pages 113-118

About this book

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants of the workshop "Positivity and Valuations", held at the Centre de Recerca Matemàtica (CRM) in Barcelona from February 22nd to 26th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and the outcome of work in groups initiated during the workshop.

The general subject is the application of valuation theory to positivity questions in algebraic geometry. The topics covered range from purely algebraic problems like finite generation of semigroups and algebras defined by valuations, and properties of the associated Poincaré series, to more geometric questions like resolution of singularities and properties of Newton-Okounkov bodies, linked with non-archimedean geometry and tropical geometry.

The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active areas of research.

Keywords

  • algebraic geometry
  • valuations
  • positivity
  • linear series
  • tropical geometry
  • nonarchimedean geometry
  • birational geometry
  • newton-okounkov bodies

Editors and Affiliations

  • Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Maria Alberich-Carramiñana

  • Departament de Matemàtiques, University Jaume I, Castellón, Spain

    Carlos Galindo

  • Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt, Germany

    Alex Küronya

  • Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Spain

    Joaquim Roé

Bibliographic Information

  • Book Title: Extended Abstracts February 2016

  • Book Subtitle: Positivity and Valuations

  • Editors: Maria Alberich-Carramiñana, Carlos Galindo, Alex Küronya, Joaquim Roé

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-00027-1

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Softcover ISBN: 978-3-030-00026-4

  • eBook ISBN: 978-3-030-00027-1

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: X, 118

  • Number of Illustrations: 10 b/w illustrations, 2 illustrations in colour

  • Topics: Algebraic Geometry, Commutative Rings and Algebras

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-00027-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)