Extended Abstracts February 2016: Positivity and Valuations

Description

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. Front Matter ....Pages i-x 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 Sufficient Conditions for the Finite Generation of Valuation Semigroups (Alex Küronya, Joaquim Roé)....Pages 9-16 From Convex Geometry of Certain Valuations to Positivity Aspects in Algebraic Geometry (Victor Lozovanu)....Pages 17-25 Non-positive at Infinity Valuations (Francisco Monserrat)....Pages 27-32 Very General Monomial Valuations on \({\varvec{\mathbb P}^2}\) and a Nagata Type Conjecture (Tomasz Szemberg)....Pages 33-37 Valuations on Equicharacteristic Complete Noetherian Local Domains (Bernard Teissier)....Pages 39-43 Desingularization by char\(\mathbf {(X)}\)-Alterations (Michael Temkin)....Pages 45-49 Semigroup and Poincaré Series for Divisorial Valuations (Willem Veys)....Pages 51-56 Computing Multiplier Ideals in Smooth Surfaces (Guillem Blanco, Ferran Dachs Cadefau)....Pages 57-63 Notes on Divisors Computing MLD’s and LCT’s (Harold Blum)....Pages 65-69 On the Containment Hierarchy for Simplicial Ideals (Magdalena Lampa-Baczyńska, Grzegorz Malara)....Pages 71-74 The Universal Zeta Function for Curve Singularities and its Relation with Global Zeta Functions (Julio José Moyano-Fernández)....Pages 75-82 Algebraic Volumes of Divisors (Carsten Bornträger, Matthias Nickel)....Pages 83-87 On Hirzebruch Type Inequalities and Applications (Justyna Szpond)....Pages 89-94 On the Completion of Normal Toric Schemes Over Rank One Valuation Rings (Alejandro Soto)....Pages 95-98 Duality on Value Semigroups (Laura Tozzo)....Pages 99-104 Notes on Local Positivity and Newton–Okounkov Bodies (Harold Blum, Grzegorz Malara, Georg Merz, Justyna Szpond)....Pages 105-111 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