Waldschmidt constant of certain sets of points with 3 supporting lines in projective plane
Abstract
The paper shows values of the initial degree and Waldschmidt constant for some special cases including several
cases of ten points with three supporting lines in projective plane. These constants represent the complexity of optimal solutions in repeated path problems that have many applications in computer science, informatics theory and telecommunications.
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References
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[14] M. Nagata, On the 14-th problem of Hilbert, Amer. J. Math. 33 (1959), 766-772.
[15] M. Nagata, On rational surfaces, II, Mem. College Sci. Univ. Kyoto Ser. A Math. 33 (1960), 271-293.
[16] A. Iarrobino. Inverse system of a symbolic power III: thin algebras and fat points, Compositio Math. 108, (1997), 319–356.
[17] H. Skoda, Estimations L2 pour l’operateur ^ et applications arithmetiques, in: Seminaire P. Lelong (Analyse), 1975/76, Lecture Notes in Mathematics 578, Springer, 1977, 314-323.
[18] Nguyen Chanh Tu, Initial degree and Waldschmidt constant of zero schemes and properties, J. Science and Technology (Issue on Information and Communications Technology), The University of Danang, to appear.
[19] Nguyen Chanh Tu, Tran Manh Hung, Waldschmidt constant of certain sets of points in projective plane with two supporting lines, J. Science and Technology, Quang Binh University, to appear.
[20] N.C. Tu, D.T. Hiep, L.N.Long, V.Thanh, Waldschmidt constant of some sets of points in projective plane, (2020), (preprint).
[21] M. Waldschmidt, Propriétés arithmétiques de fonctions de plusieurs variables II, Séminaire P. Lelong (Analyse), 1975-76, Lecture Notes Math. 578, Springer-Verlag, 1977, 108-135.
[22] M. Waldschmidt, Nombres transcendants et groupes algébriques, Astérisque 69/70, Socéte Mathématiqué de France, 1979
[2] G. V. Chudnovsky, Singular points on complex hypersurfaces and multidimensional Schwarz Lemma, Seminaire de Théorie des Nombres, Paris 1979-80, Séminaire Delange-Pisot-Poitou, Progress in Math vol. 12, M-J Bertin, editor, Birkhauser, Boston-Basel-Stutgart (1981).
[3] S. M. Cooper and B. Harbourne, Regina Lectures On Fat Points, Springer Proceedings in Mathematics and Statistics, Vol. 76 (2014), ISBN: 978-1-4939-0625-3.
[4] M. Dumnicki, Symbolic powers of ideals of generic points in Pn, J. Pure Appl. Algebra 216 (2012), 1410-1417.
[5] M. Dumnicki, H.T. Gasinska, A containment result in Pn and the Chudnovsky conjecture, Proc. Amer. Math. Soc. 145, (2017), 3689-3694.
[6] L. Ein, R. Lazarsfeld, and K.E. Smith, Uniform behavior of symbolic powers of ideals, Invent. Math., 144 (2001), 241-252.
[7] H. Esnault and E. Viehweg, Sur une minoration du degré d’hypersurfaces s’annulant en certains points, Math. Ann. 263 (1983), no. 1, 75-86.
[8] L. Evain, On the postulation of sd fat points in Pd , J. Algebra 285 (2005), 516-530.
[9] L. Fouli, P. Mantero, Y. Xie, Chudnovsky’s Conjecture for very general points in Pnk , J. of Algebra, 498 (2018), 211-227.
[10] R. Harshorne, Algebraic Geometry, Spinger-Verlag, (1977)
[11] B. Harbourne and C. Huneke Are symbolic powers highly evolved?, J. Ramanujan Math. Soc. 28A (2013), 247-266.
[12] M. Hochster and C. Huneke, Comparison of symbolic and ordinary powers of ideals, Invent. Math. 147 (2002), no. 2, 349-369
[13] M. Janssen, (2013) Symbolic Powers of Ideals in k[PN], Dissertations, Theses and Student Research Papers in Mathematics. 41, Lincoln, Nebraska.
[14] M. Nagata, On the 14-th problem of Hilbert, Amer. J. Math. 33 (1959), 766-772.
[15] M. Nagata, On rational surfaces, II, Mem. College Sci. Univ. Kyoto Ser. A Math. 33 (1960), 271-293.
[16] A. Iarrobino. Inverse system of a symbolic power III: thin algebras and fat points, Compositio Math. 108, (1997), 319–356.
[17] H. Skoda, Estimations L2 pour l’operateur ^ et applications arithmetiques, in: Seminaire P. Lelong (Analyse), 1975/76, Lecture Notes in Mathematics 578, Springer, 1977, 314-323.
[18] Nguyen Chanh Tu, Initial degree and Waldschmidt constant of zero schemes and properties, J. Science and Technology (Issue on Information and Communications Technology), The University of Danang, to appear.
[19] Nguyen Chanh Tu, Tran Manh Hung, Waldschmidt constant of certain sets of points in projective plane with two supporting lines, J. Science and Technology, Quang Binh University, to appear.
[20] N.C. Tu, D.T. Hiep, L.N.Long, V.Thanh, Waldschmidt constant of some sets of points in projective plane, (2020), (preprint).
[21] M. Waldschmidt, Propriétés arithmétiques de fonctions de plusieurs variables II, Séminaire P. Lelong (Analyse), 1975-76, Lecture Notes Math. 578, Springer-Verlag, 1977, 108-135.
[22] M. Waldschmidt, Nombres transcendants et groupes algébriques, Astérisque 69/70, Socéte Mathématiqué de France, 1979
Published
2021-06-29
How to Cite
NGUYEN, Tu Chanh; HIEP, Dang Tuan.
Waldschmidt constant of certain sets of points with 3 supporting lines in projective plane.
Journal of Science and Technology: Issue on Information and Communications Technology, [S.l.], v. 19, n. 6.2, p. 52-55, june 2021.
ISSN 1859-1531.
Available at: <http://ict.jst.udn.vn/index.php/jst/article/view/127>. Date accessed: 16 apr. 2024.
doi: https://doi.org/10.31130/ict-ud.2021.127.
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