Extended Abstracts February 2016

1. Front Matter

   Pages i-x

   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

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.

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

• 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

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