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Rational Surfaces with Anticanonical Divisor not Reduced Cover

Rational Surfaces with Anticanonical Divisor not Reduced

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică
Volume 21 (2013): Issue 3 (November 2013)
By: Jesús Adrian Cerda Rodriguez,  Mustapha Lahyane,  Osvaldo Osuna-Castro,  Gioia Failla and  Israel Moreno-Mejia  
Open Access
|Mar 2014

References

  1. [1] W. Barth, C. Peters, A. Van de Ven, Compact Complex Surfaces, Berlin, Springer 1984.10.1007/978-3-642-96754-2
    Search in Google Scholar
  2. [2] A. Campillo, G. Gonzalez-Sprinberg, On characteristic cones, clusters and chains of infinitely near points, in: Brieskorn Conference Volume, in: Progr. Math., vol. 162, Birkhäuser, 1998.10.1007/978-3-0348-8770-0_13
    Search in Google Scholar
  3. [3] A. Campillo, O. Piltant, A. Reguera, Cones of Curves and of Line Bun­dles on Surfaces Associated with Curves Having one Point at Infinity, Proceedings of the London Mathematical Society, Vol.84, Issue 03 (2002), 559-580.
    Search in Google Scholar
  4. [4] A. Campillo, O. Piltant, A. Reguera, Cones of curves and of line bundles at infinity. Journal of Algebra 293, 503-542 (2005).10.1016/j.jalgebra.2005.02.021
    Search in Google Scholar
  5. [5] C. Galindo, F. Monserrat, The cone of curves associated to a plane con­figuration, Commentarii Mathematici Helvetici 80 (2005), 75-93.10.4171/CMH/5
    Search in Google Scholar
  6. [6] C. Galindo, F. Monserrat, The cone of curves of Line Bundles of a Ratio­nal Surface, International Journal of Mathematics. Vol. 15, No. 4 (2004), 393-407.
    Search in Google Scholar
  7. [7] G. Failla, M. Lahyane, G. Molica Bisci, On the finite generation of the monoid of effective divisor classes on rational surfaces of type (n, m), Atti dell' Accademia Peloritana dei Pericolanti Classe di Scienze Fisiche, Matematiche e Naturali Vol. LXXXIV, C1A0601001 (2006)10.1142/9789812707499_0022
    Search in Google Scholar
  8. [8] G. Failla, M. Lahyane, G. Molica Bisci, The finite generation of the monoid of effective divisor classes on Platonic rational surfaces. Singu­larity Theory, Proceedings of the 2005 Marseille Singularity School and Conference, 565-576, CIRM, Marseille, France. World Scientific Publish­ing Co. 2007.10.1142/9789812707499_0022
    Search in Google Scholar
  9. [9] G. Failla, M. Lahyane, G. Molica Bisci, Rational Surfaces of Kodaira type IV, Bollettino dell’Unione Matematica Italiana, Sezione B; articoli di ricerca matematica, Volume 10, Number 3 (2007), pages 741 - 750.
    Search in Google Scholar
  10. [10] B. Harbourne, Blowings-up of P2 and their blowings-down, Duke Mathe­matical Journal, 52:1 (1985), 129 - 148.10.1215/S0012-7094-85-05208-1
    Search in Google Scholar
  11. [11] B. Harbourne, Points in good position in P2, Zero-dimensional schemes, Proceedings of the International Conference held in Ravello, Italy, June 8-13, 1992, De Gruyter, Berlin, 1994.10.1515/9783110889260-018
    Search in Google Scholar
  12. [12] B. Harbourne, Rational surfaces with K2 > 0, Proceedings of the Amer­ican Mathematical Society, Volume 124 Number 3 (March 1996), 727 - 733.10.1090/S0002-9939-96-03226-1
    Search in Google Scholar
  13. [13] B. Harbourne, Anticanonical rational surfaces, Transactions of the Amer­ican Mathematical Society, Volume 349 Number 3 (1997), 1191 - 1208.
    Search in Google Scholar
  14. [14] B. Harbourne, Free resolutions of fat point ideals on P2, Journal of Pure and Applied Algebra, 125 (1998), 213 - 234.10.1016/S0022-4049(96)00126-0
    Search in Google Scholar
  15. [15] B. Harbourne, R. Miranda, Exceptional curves on rational numerically elliptic surfaces, Journal of Algebra, 128 (1990), 405 - 433.10.1016/0021-8693(90)90031-I
    Search in Google Scholar
  16. [16] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer Verlag (1977).10.1007/978-1-4757-3849-0
    Search in Google Scholar
  17. [17] M. Lahyane, Exceptional curves on rational surfaces having K2 > 0, Comptes Rendus Mathematique, Volume 338, Issue 11, 1 June 2004, 873 - 878.10.1016/j.crma.2004.03.029
    Search in Google Scholar
  18. [18] M. Lahyane, Rational surfaces having only a finite number of exceptional curves, Mathematische Zeitschrift, Volume 247 Number 1 (May 2004), 213 - 221.10.1007/s00209-002-0474-y
    Search in Google Scholar
  19. [19] M. Lahyane, Exceptional curves on smooth rational surfaces with -K not nef and of self-intersection zero, Proceedings of the American Mathemat­ical Society, 133 (2005), 1593 - 1599.10.1090/S0002-9939-04-07693-2
    Search in Google Scholar
  20. [20] M. Lahyane, B. Harbourne, Irreducibility of -1-classes on anticanonical rational surfaces and finite generation of the effective monoid, Pacific Journal of Mathematics, Volume 218 Number 1 (2005), 101 - 114.
    Search in Google Scholar
  21. [21] M. Lahyane, On the finite generation of the effective monoid of ratio­nal surfaces, Journal of Pure and Applied Algebra, Volume 214, Issue 7 (2010), 1217- 1240.
    Search in Google Scholar
  22. [22] E. Looijenga, Rational surfaces with an anticanonical cycle, Annals of Mathematics, 114 no. 2 (1981), 267 - 322.
    Search in Google Scholar
  23. [23] R. Miranda, U. Persson, On extremal rational elliptic surfaces, Mathe­matische Zeitschrift, 193 (1986), 537 - 558.10.1007/BF01160474
    Search in Google Scholar
  24. [24] M. Nagata, On rational surfaces, II, Memoirs of the College of Science, University of Kyoto, Series A 33 (1960), no. 2, 271 - 293.
    Search in Google Scholar
  25. [25] J. Rosoff, Effective divisor classes and blowings-up of P2, Pacific Journal of Mathematics, 89 (2) (1980), 419 - 42910.2140/pjm.1980.89.419
    Search in Google Scholar
DOI: https://doi.org/10.2478/auom-2013-0055 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
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Language: English
Page range: 229 - 240
Published on: Mar 5, 2014
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year
Keywords:
Rational surfaces,
Neron-Severi group,
Blowing-up,
Monoid of effective divisor classes
Related subjects:
Mathematics,
General mathematics

© 2014 Jesús Adrian Cerda Rodriguez, Mustapha Lahyane, Osvaldo Osuna-Castro, Gioia Failla, Israel Moreno-Mejia, published by Ovidius University of Constanta
This work is licensed under the Creative Commons License.

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