2026-04-17T15:53:48Zhttps://recercat.cat/oai/request

oai:recercat.cat:2072/4797322025-07-29T23:34:26Zcom_2072_98col_2072_378192

Newton-Okounkov bodies and Picard numbers on surfaces Moyano Fernández, Julio José 4u Universitat Jaume I. Departamento de Matemática Nickel, Matthias Roé Vellvé, Joaquim Valuation Blowup Newton-Okounkov body Algebraic surface Picard number We study the shapes of all Newton-Okounkov bodies ∆v(D) of a given big divisor D on a surface S with respect to all rank 2 valuations v of K(S). We obtain upper bounds for, and in many cases we determine exactly, the possible numbers of vertices of the bodies ∆v(D). The upper bounds are expressed in terms of Picard numbers and they are birationally invariant, as they do not depend on the model S˜ where the valuation v becomes a flag valuation. We also conjecture that the set of all Newton-Okounkov bodies of a single ample divisor D determines the Picard number of S, and prove that this is the case for Picard number 1, by an explicit characterization of surfaces of Picard number 1 in terms of Newton-Okounkov bodies. 2025 Article https://ddd.uab.cat/record/304450 urn:10.5565/PUBLMAT6912501 urn:oai:ddd.uab.cat:304450 urn:oai:raco.cat:article/433253 urn:articleid:20144350v69n1p3 urn:oai:egreta.uab.cat:publications/57443c68-7c83-4e84-8534-b72ceda78e99 eng ; Publicacions matemàtiques ; Vol. 69 Núm. 1 (2025), p. 3-25 open access Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets. https://rightsstatements.org/vocab/InC/1.0/ application/pdf