Rational Surfaces with Anticanonical Divisor not Reduced

[1] W. Barth, C. Peters, A. Van de Ven, Compact Complex Surfaces, Berlin, Springer 1984.10.1007/978-3-642-96754-2Search in Google Scholar

[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_13Search in Google Scholar

[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] 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.2005.02.021Search in Google Scholar

[5] C. Galindo, F. Monserrat, The cone of curves associated to a plane con­figuration, Commentarii Mathematici Helvetici 80 (2005), 75-93.10.4171/CMH/5Search in Google Scholar

[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] 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_0022Search in Google Scholar

[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_0022Search in Google Scholar

[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] B. Harbourne, Blowings-up of P² and their blowings-down, Duke Mathe­matical Journal, 52:1 (1985), 129 - 148.10.1215/S0012-7094-85-05208-1Search in Google Scholar

[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, 1994.10.1515/9783110889260-018Search in Google Scholar

[12] B. Harbourne, Rational surfaces with K² > 0, Proceedings of the Amer­ican Mathematical Society, Volume 124 Number 3 (March 1996), 727 - 733.10.1090/S0002-9939-96-03226-1Search in Google Scholar

[13] B. Harbourne, Anticanonical rational surfaces, Transactions of the Amer­ican Mathematical Society, Volume 349 Number 3 (1997), 1191 - 1208.Search in Google Scholar

[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)00126-0Search in Google Scholar

[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-ISearch in Google Scholar

[16] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer Verlag (1977).10.1007/978-1-4757-3849-0Search in Google Scholar

[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.2004.03.029Search in Google Scholar

[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-ySearch in Google Scholar

[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/S0002-9939-04-07693-2Search in Google Scholar

[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] 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] E. Looijenga, Rational surfaces with an anticanonical cycle, Annals of Mathematics, 114 no. 2 (1981), 267 - 322.Search in Google Scholar

[23] R. Miranda, U. Persson, On extremal rational elliptic surfaces, Mathe­matische Zeitschrift, 193 (1986), 537 - 558.10.1007/BF01160474Search in Google Scholar

[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] J. Rosoff, Effective divisor classes and blowings-up of P², Pacific Journal of Mathematics, 89 (2) (1980), 419 - 42910.2140/pjm.1980.89.419Search in Google Scholar