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Extended Abstracts February 2016

Positivity and Valuations

  • Conference proceedings
  • © 2018

Overview

Editors:
  1. Maria Alberich-Carramiñana

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

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  2. Carlos Galindo

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

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  3. Alex Küronya

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

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  4. Joaquim Roé

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

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  • 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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Table of contents (18 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  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. Sufficient Conditions for the Finite Generation of Valuation Semigroups

    • Alex Küronya, Joaquim Roé
    Pages 9-16

  4. From Convex Geometry of Certain Valuations to Positivity Aspects in Algebraic Geometry

    • Victor Lozovanu
    Pages 17-25

  5. Non-positive at Infinity Valuations

    • Francisco Monserrat
    Pages 27-32

  6. Very General Monomial Valuations on \({\varvec{\mathbb P}^2}\) and a Nagata Type Conjecture

    • Tomasz Szemberg
    Pages 33-37

  7. Valuations on Equicharacteristic Complete Noetherian Local Domains

    • Bernard Teissier
    Pages 39-43

  8. Desingularization by char\(\mathbf {(X)}\)-Alterations

    • Michael Temkin
    Pages 45-49

  9. Semigroup and Poincaré Series for Divisorial Valuations

    • Willem Veys
    Pages 51-56

  10. Computing Multiplier Ideals in Smooth Surfaces

    • Guillem Blanco, Ferran Dachs Cadefau
    Pages 57-63

  11. Notes on Divisors Computing MLD’s and LCT’s

    • Harold Blum
    Pages 65-69

  12. On the Containment Hierarchy for Simplicial Ideals

    • Magdalena Lampa-Baczyńska, Grzegorz Malara
    Pages 71-74

  13. The Universal Zeta Function for Curve Singularities and its Relation with Global Zeta Functions

    • Julio José Moyano-Fernández
    Pages 75-82

  14. Algebraic Volumes of Divisors

    • Carsten Bornträger, Matthias Nickel
    Pages 83-87

  15. On Hirzebruch Type Inequalities and Applications

    • Justyna Szpond
    Pages 89-94

  16. On the Completion of Normal Toric Schemes Over Rank One Valuation Rings

    • Alejandro Soto
    Pages 95-98

  17. Duality on Value Semigroups

    • Laura Tozzo
    Pages 99-104

  18. Notes on Local Positivity and Newton–Okounkov Bodies

    • Harold Blum, Grzegorz Malara, Georg Merz, Justyna Szpond
    Pages 105-111

  19. 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
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Keywords

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.

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: 978-3-030-00026-4Published: 04 November 2018

  • eBook ISBN: 978-3-030-00027-1Published: 03 November 2018

  • 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

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