Linear subspaces, symbolic powers and Nagata type conjectures

• Autores: Marcin Dumnicki, Brian Harbourne, Tomasz Szemberg, Halszka Tutaj-Gasinska
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 252, Nº 1, 2014, págs. 471-491
• Idioma: inglés
• DOI: 10.1016/j.aim.2013.10.029
• Texto completo no disponible (Saber más ...)
• Referencias bibliográficas
  • J. Alexander, A. Hirschowitz, Polynomial interpolation in several variables, J. Algebraic Geom. 4 (1995) 201–222.
  • T. Bauer, S. Di Rocco, B. Harbourne, M. Kapustka, A. Knutsen, W. Syzdek, T. Szemberg, A primer on Seshadri constants, in: D.J. Bates, G.-M....
  • C. Bocci, Special effect varieties in higher dimension, Collect. Math. 56 (2005) 299–326.
  • C. Bocci, B. Harbourne, Comparing powers and symbolic powers of ideals, J. Algebraic Geom. 19 (2010) 399–417.
  • G.V. Chudnovsky, Singular points on complex hypersurfaces and multidimensional Schwarz lemma, in: M.-J. Bertin (Ed.), Séminaire de Théorie...
  • S.D. Cutkosky, J. Herzog, N.V. Trung, Asymptotic behaviour of the Castelnuovo–Mumford regularity, Compos. Math. 118 (1999) 243–261.
  • H. Derksen, Hilbert series of subspace arrangements, J. Pure Appl. Algebra 209 (2007) 91–98.
  • M. Dumnicki, An algorithm to bound the regularity and nonemptiness of linear systems in Pn, J. Symbolic Comput. 44 (10) (2009) 1448–1462.
  • L. Ein, R. Lazarsfeld, K.E. Smith, Uniform behavior of symbolic powers of ideals, Invent. Math. 144 (2001) 241–252.
  • H. Esnault, E. Viehweg, Sur une minoration du degré d’hypersurfaces s’annulant en certains points, Math. Ann. 263 (1983) 75–86.
  • L. Evain, On the postulation of sd fat points in Pd, J. Algebra 285 (2005) 516–530.
  • A. Geramita, B. Harbourne, J. Migliore, Classifying Hilbert functions of fat point subschemes in P2, Collect. Math. 60 (2) (2009) 159–192.
  • A. Geramita, B. Harbourne, J. Migliore, Star configurations in Pn, J. Algebra 376 (2013) 279–299.
  • E. Guardo, B. Harbourne, A. Van Tuyl, Asymptotic resurgences for ideals of positive dimensional subschemes of projective space, Adv. Math....
  • E. Guardo, B. Harbourne, A. Van Tuyl, Symbolic powers versus regular powers of ideals of general points in P1 ×P1, Canad. J. Math. 65 (2013)...
  • B. Harbourne, C. Huneke, Are symbolic powers highly evolved?, J. Ramanujan Math. Soc. 28 (2013) 311–330.
  • J. Harris, Algebraic Geometry. A First Course, Grad. Texts in Math., vol. 133, Springer-Verlag, New York, 1992.
  • R. Hartshorne, A. Hirschowitz, Droites en position générale dans l’espace projectif, in: Algebraic Geometry, La Rábida, 1981, in: Lecture...
  • M. Hochster, C. Huneke, Comparison of symbolic and ordinary powers of ideals, Invent. Math. 147 (2) (2002) 349–369.
  • A. Iarrobino, Inverse system of a symbolic power III: thin algebras and fat points, Compos. Math. 108 (1997) 319–356.
  • V. Kodiyalam, Asymptotic behaviour of Castelnuovo–Mumford regularity, Proc. Amer. Math. Soc. 128 (2000) 407–411.
  • A. Laface, L. Ugaglia, Elementary (−1)-curves of P3, Comm. Algebra 35 (2007) 313–324.
  • R. Lazarsfeld, Positivity in Algebraic Geometry I–II, Ergeb. Math. Grenzgeb., Vols. 48–49, Springer Verlag, Berlin, 2004.
  • R. Lazarsfeld, A short course on multiplier ideals, in: Analytic and Algebraic Geometry, in: IAS/Park City Math. Ser., vol. 17, Amer. Math....
  • M. Maggesi, On the quantum cohomology of blow-ups of projective spaces along linear subspaces, preprint, arXiv:math/9810150v2, 2000.
  • M. Nagata, On the 14-th problem of Hilbert, Amer. J. Math. 81 (1959) 766–772.
  • M. Waldschmidt, Propriétés arithmétiques de fonctions de plusieurs variables II, in: Séminaire P. Lelong (Analyse), 1975–1976, in: Lecture...