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Asymptotic Hilbert polynomial and a bound for Waldschmidt constants

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  • In the paper we give a method to compute an upper bound for the Waldschmidt constants of a wide class of ideals. This generalizes the result obtained by Dumnicki, Harbourne, Szemberg and Tutaj-Gasińska, Adv. Math. 2014, [5]. Our bound is given by a root of a suitable derivative of a certain polynomial associated with the asymptotic Hilbert polynomial.
    Mathematics Subject Classification: 13P10, 14N20.


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  • [1]

    Th. Bauer, S. Di Rocco, B. Harbourne, M. Kapustka, A. L. Knutsen, W. Syzdek and T. Szemberg, A primer on Seshadri constants, in Interactions of Classical and Numerical Algebraic Geometry, Proceedings of a conference in honor of A. J. Sommese, held at Notre Dame, May 22-24 2008 (eds. D. J. Bates, G.-M. Besana, S. Di Rocco and C. W. Wampler), Contemporary Mathematics, 496, American Mathematical Society, Providence, RI, 2009, 362pp.doi: 10.1090/conm/496.


    C. Bocci, S. Cooper and B. Harbourne, Containment results for ideals of various configurations of points in $\mathbbP^N$, J. Pure Appl. Algebra, 218 (2014), 65-75.doi: 10.1016/j.jpaa.2013.04.012.


    C. Bocci and B. Harbourne, Comparing powers and symbolic powers of ideals, J. Algebraic Geometry, 19 (2010), 399-417.doi: 10.1090/S1056-3911-09-00530-X.


    C. Bocci and B. Harbourne, The resurgence of ideals of points and the containment problem, Proc. Amer. Math. Soc., 138 (2010), 1175-1190.doi: 10.1090/S0002-9939-09-10108-9.


    M. Dumnicki, B. Harbourne, T. Szemberg and H. Tutaj-Gasińska, Linear subspaces, symbolic powers and Nagata type conjectures, Adv. Math., 252 (2014), 471-491.doi: 10.1016/j.aim.2013.10.029.


    M. Dumnicki, T. Szemberg, J. Szpond and H. Tutaj-Gasińska, Symbolic generic initial systems of star configurations, J. Pure Appl. Algebra, 219 (2015), 1073–-1081.doi: 10.1016/j.jpaa.2014.05.035.


    M. Dumnicki, J. Szpond and H. Tutaj-Gasińska, Asymptotic Hilbert polynomials and limiting shapes, J. Pure Appl. Algebra, 219 (2015), 4446-4457.doi: 10.1016/j.jpaa.2015.02.026.


    L. Ein, R. Lazarsfeld, M. Mustaţă, M. Nakamaye and M. Popa, Asymptotic invariants of base loci, Ann. Inst. Fourier (Grenoble), 56 (2006), 1701-1734.doi: 10.5802/aif.2225.


    L. Ein, R. Lazarsfeld, M. Mustaţă, M. Nakamaye and M. Popa, Restricted volumes and base loci of linear series, Amer. J. Math., 131 (2009), 607-651.doi: 10.1353/ajm.0.0054.


    L. Ein, R. Lazarsfeld and K. Smith, Uniform bounds and symbolic powers on smooth varieties, Invent. Math., 144 (2001), 241-252.doi: 10.1007/s002220100121.


    D. Eisenbud, Commutative Algebra. With a View Toward Algebraic Geometry, Springer-Verlag, New York, 1995.doi: 10.1007/978-1-4612-5350-1.


    H. Esnault and E. Viehweg, Sur une minoration du degré d'hypersurfaces s'annulant en certains points, Math. Ann., 263 (1983), 75-86.doi: 10.1007/BF01457085.


    A. Galligo, Á propos du théorème de préparation de Weierstrass, in Fonctions de Plusieurs Variables Complexes, Lecture Notes in Math., Vol. 409, Springer, Berlin, 1974, 543-579.


    A. V. Geramita, B. Harbourne and J. Migliore, Star configurations in $\mathbbP^n$, J. Algebra, 376 (2013), 279-299.doi: 10.1016/j.jalgebra.2012.11.034.


    M. L. Green, Generic initial ideals, in Six Lectures on Commutative Algebra, Progr. Math., 166, Birkhäuser, Basel, 1998, 119-186.


    J. Herzog and H. Srinivasan, Bounds for multiplicities, Trans. Amer. Math. Soc., 350 (1998), 2879-2902.doi: 10.1090/S0002-9947-98-02096-0.


    H. Hochster and C. Huneke, Comparison of symbolic and ordinary powers of ideals, Invent. Math., 147 (2002), 349-369.doi: 10.1007/s002220100176.


    S. Mayes, The asymptotic behaviour of symbolic generic initial systems of generic points, J. Pure Appl. Alg., 218 (2014), 381-390.doi: 10.1016/j.jpaa.2013.06.002.


    S. Mayes, The limiting shape of the generic initial system of a complete intersection, Comm. Algebra, 42 (2014), 2299-2310.doi: 10.1080/00927872.2012.758271.


    M. Mustaţă, On multiplicities of graded sequences of ideals, J. Algebra, 256 (2002), 229-249.doi: 10.1016/S0021-8693(02)00112-6.


    S. Sullivant, Combinatorial symbolic powers, J. Algebra, 319 (2008), 115-142.doi: 10.1016/j.jalgebra.2007.09.024.

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