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    Título
    Minimal plane valuations
    Autor
    Galindo, Carlos
    Monserrat, Francisco
    Moyano Fernández, Julio José
    Año del Documento
    2018
    Editorial
    American Mathematical Society
    Descripción
    Producción Científica
    Documento Fuente
    Journal of Algebraic Geometry, 2018, vol. 27. p. 751-783
    Resumo
    We consider the value ˆμ( ) = limm→∞ m−1a(mL), where a(mL) is the last value of the vanishing sequence of H0(mL) along a divisorial or irrational valuation centered at OP2,p, L (respectively, p) being a line (respectively, a point) of the projective plane P2 over an algebraically closed field. This value contains, for valuations, similar information as that given by Seshadri constants for points. It is always true that ˆμ( ) ≥ p1/vol( ) and minimal valuations are those satisfying the equality. In this paper, we prove that the Greuel-Lossen-Shustin Conjecture implies a variation of the Nagata Conjecture involving minimal valuations (that extends the one stated in [15] to the whole set of divisorial and irrational valuations of the projective plane) which also implies the original Nagata’s conjecture. We also provide infinitely many families of minimal very general valuations with an arbitrary number of Puiseux exponents, and an asymptotic result that can be considered as evidence in the direction of the above mentioned conjecture.
    Palabras Clave
    Plane valuations
    Valoración de planos
    Algebra
    Álgebra
    ISSN
    1534-7486
    Revisión por pares
    SI
    DOI
    10.1090/jag/722
    Patrocinador
    Ministerio de Economía, Industria y Competitividad ( grants MTM2012-36917-C03-03 / MTM2015-65764-C3-2-P / MTM2016-81735- REDT)
    Universitat Jaume I (grant P1-1B2015-02)
    Version del Editor
    http://www.ams.org/journals/jag/2018-27-04/S1056-3911-2018-00722-2/
    Propietario de los Derechos
    © 2018 American Mathematical Society
    Idioma
    eng
    URI
    http://uvadoc.uva.es/handle/10324/35952
    Derechos
    openAccess
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    • IMUVA - Artículos de Revista [104]
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