References
- [1] M. Artebani, A. Laface, Cox rings of surfaces and the anticanonical Iitaka dimension. Adv. Math. 226 no. 6 (2011), 5252–5267.
- [2] A. Campillo, G. Gonzalez-Sprinberg, F. Monserrat, Configurations of infinitely near points.São Paulo Journal of Mathematical Sciences 3 no.1 (2009), 115–160.10.11606/issn.2316-9028.v3i1p115-160
- [3] A. Campillo, O. Piltant, A. J. Reguera-López, Conesofcurves andofline bundles on surfaces associated with curves having one place at infinity. Proc. London Math. Soc. 84(3) (2002), 559–580.10.1112/S0024611502013394
- [4] A. Campillo, O. Piltant, A. J. Reguera-López, Cones of curves and of line bundles at “infinity”. J. Algebra 293 (2005), 503–542.
- [5] J. A. Cerda Rodríguez, G. Failla, M. Lahyane, O. Osuna-Castro, Fixed loci of the Anticanonical linear systems of Anticanonical Rational Surfaces. Balkan Journal of Geometry and its applications 17 (2012), 1–8.
- [6] D. Cox, The homogeneous coordinate ring of a toric variety.J.Algebraic Geom. 4 (1995), no. 1, 17–50.
- [7] B.L.DeLaRosaNavarro, Códigos Algebraico Geométricos en Dimensión Superior y la Finitud de los Anillos de Cox de Superficies Racionales. Ph.D. Thesis, University of Michoacán, Michoacán 2013.
- [8] B. L. De La Rosa-Navarro, G. Failla, J.B. Frías-Medina, M. Lahyane, R. Utano, Eckardt surfaces, Fundamenta Mathematicae 243 (2018), 195–208.10.4064/fm424-12-2017
- [9] B. L. De La Rosa-Navarro, G. Failla, J.B. Frías-Medina, M. Lahyane, R. Utano, Platonic surfaces,in: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics: Festschrift for Antonio Campillo on the Occasion of his 65th Birthday, Greuel, G.M., Narváez Macarro, M., Xambó-Descamps, S. (2018), Springer Nature Switzerland AG, Chapter 12, 319–342.
- [10] B. L. De La Rosa-Navarro, J.B. Frías-Medina, M. Lahyane, I. Moreno-Mejía, O. Osuna-Castro, A geometric criterion for the finite generation of the Cox rings of projective surfaces, Revista Matematica Iberoamericana 31 (2015), 1131-1140.10.4171/RMI/878
- [11] B. L. De La Rosa-Navarro, J.B. Frías-Medina, M. Lahyane, Rational surfaces with finitely generated Cox rings and very high Picard numbers, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales -Serie A: Matemáticas 111 (2017), 297-306.
- [12] B. L. De La Rosa-Navarro, J.B. Frías-Medina, M. Lahyane, Platonic Harbourne-Hirschowitz Rational Surfaces, Mediterranean Journal of Mathematics 17 (2020), no. 5, Paper No. 154, 21 pp. DOI: 10.1007/s00009-020-01593-5.10.1007/s00009-020-01593-5
- [13] M. Demazure, Surfaces de Del Pezzo II - V,in: Séminaire sur les Singularités des Surfaces, Demazure, M.; Pinkham, H.; Teissier, B. Eds. Springer: Heidelberg, 1980, 23–69.
- [14] 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 Cl. Sci. Fis., Mat. Natur. (2006), LXXXIV, DOI:10.1478/C1A0601001
- [15] G. Failla, M. Lahyane, G. Molica Bisci, The finite generation of the monoid of effective divisor classes on Platonic rational surfaces, in: Singularity Theory; Chéniot D., Dutertre N., Murolo, C., Trotman D., Pichon, A., Eds; World Scientific Publishing Company, - Hackensack, NJ (2007), 565–576.10.1142/9789812707499_0022
- [16] G. Failla, M. Lahyane, G. Molica Bisci, Rational surfaces of Kodaira type IV, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 8, 10 (2007), 741–750.
- [17] J. B. Frías-Medina, M. Lahyane, Harbourne-Hirschowitz surfaces whose anticanonical divisors consist only of three irreducible components, Internat. J. Math. 29 (2018), no. 12, 1850072, 19 pp. DOI: 10.1142/S0129167X1850072610.1142/S0129167X18500726
- [18] J. B. Frías-Medina, M. Lahyane, The effective monoids of the blow-ups of Hirzebruch surfaces at points in general position, Rendiconti del Circolo Matematico di Palermo Series 2 70 (2021), no. 1, 167–197.
- [19] C. Galindo, F. Monserrat, On the cone of curves and of line bundles of a rational surface. Internat. J. Math. 15 (2004), no. 4, 393–407.
- [20] C. Galindo, F. Monserrat, The total coordinate ring of a smooth projective surface, J. Algebra 284 (2005), 91–101.10.1016/j.jalgebra.2004.10.004
- [21] C. Galindo, F. Monserrat, The cone of curves associated to a plane configuration. Comment. Math. Helv. 80 (2005), no. 1, 75–93.
- [22] C. Galindo, F. Monserrat, The cone of curves and the Cox ring of rational surfaces given by divisorial valuations, Adv. Math. 290 (2016), 1040–106110.1016/j.aim.2015.12.015
- [23] C. Galindo, F. Monserrat, C. J. Moreno-Ávila, Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces.Rev.Mat.Complut. 33(2) (2020), 349–372.10.1007/s13163-019-00319-w
- [24] C. Galindo, F. Monserrat, J. J. Moyano-Fernández, M. Nickel, Newton-Okounkov bodies of exceptional curve valuations. Rev. Mat. Iberoam. 36(7) (2020), 2147–2182.10.4171/rmi/1195
- [25] S. Giuffrida, R. Maggioni, The global ring of a smooth projective surface. Le Matematiche 55(1) (2000), 133–159.
- [26] B. Harbourne, Blowings-up of ℙ2k and their blowings-down. Duke Math. J. 52 (1985), no. 1, 129–148.
- [27] B. Harbourne, Rational surfaces with K2 > 0. Proc. Amer. Math. Soc. 124 (1996), 727–733.10.1090/S0002-9939-96-03226-1
- [28] B. Harbourne, Anticanonical rational surfaces. Trans. Amer. Math. Soc. 349 (1997), 1191–1208.10.1090/S0002-9947-97-01722-4
- [29] B. Harbourne, Global aspects of the geometry of surfaces. Ann. Univ. Paedagog. Crac. Stud. Math. 9 (2010), 5–41.
- [30] B. Harbourne, Free resolutions of fat point ideals on ℙ2. J. Pure Appl. Algebra 125 (1998), 213–234.10.1016/S0022-4049(96)00126-0
- [31] B. Harbourne, R. Miranda, Exceptional curves on rational numerically elliptic surfaces. J. Algebra 128 (1990), 405-433.
- [32] R. Hartshorne, Algebraic geometry. Springer-Verlag: New York-Heidelberg, 1977.10.1007/978-1-4757-3849-0
- [33] J. Hausen, Cox rings and combinatorics II. Mosc. Math. J. 8 (2008), 711–757.
- [34] Y. Hu, S. Keel, Mori dream spaces and GIT. Michigan Math. J. 48 (2000), 331–348.
- [35] M. Lahyane, Rational surfaces having only a finite number of exceptional curves, Math. Z. 247 (2004), 213–221.10.1007/s00209-002-0474-y
- [36] M. Lahyane, Exceptional curves on smooth rational surfaces with −K not nef and of self-intersection zero. Proc. Amer. Math. Soc. 133 (2005), 1593–1599.
- [37] M. Lahyane, On the finite generation of the effective monoid of rational surfaces. J. Pure Appl. Algebra 214 (2010), 1217–1240.
- [38] M. Lahyane, B. Harbourne, Irreducibility of −1−classes on anticanonical rational surfaces and finite generation of the effective monoid. Pacific J. Math. 218 (2005), 101–114.
- [39] R. Miranda, U. Persson, On extremal rational elliptic surfaces.Math. Z. 193(4) (1986), 537–558.10.1007/BF01160474
- [40] C. J. Moreno-Ávila, Global geometry of surfaces defined by non-positive nad negative at infinity valuations. Ph.D. Thesis, University of Jaume I, 2021.
- [41] F. Monserrat, Curves having one place at infinity and linear systems on rational surfaces. J. Pure Appl. Algebra 211(3) (2007), 685–701.10.1016/j.jpaa.2007.03.008
- [42] F. Monserrat, Fibers of pencils of curves on smooth surfaces. Internat. J. Math. 22 (2011), no. 10, 1433–1437.
- [43] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math, 116, 133–176.10.2307/2007050
- [44] M. Nagata, On rational surfaces, II. Memoirs of the College of Science, University of Kyoto, Series A 33 (1960), 271–293.
- [45] J. C. Ottem, On the Cox ring of ℙ2 blown up in points on a line.Math. Scand. 109 (2011), 22–30.
- [46] J. Rosoff, On the Semi-group of Effective Divisor Classes of an Algebraic Variety: The Question of Finite Generation. Ph.D. Thesis, University of California, Berkeley (1978)
- [47] J. Rosoff, Effective divisor classes and blowings-up of ℙ2. Pacific J. Math. 89 (1980), 419–429.
- [48] J. Rosoff, Effective divisor classes on a ruled surface. Pacific J. Math. 202 (2002), 119–124.
- [49] D. Testa, A. Várilly-Alvarado, M. Velasco, Big rational surfaces.Math. Ann. 351 (2011), 95–107.