Abhyankar, S.S., Moh, T.T.: Newton-Puiseux expansion and generalized Tschirnhausen transformation. I, II. J. Reine Angew. Math. 260, 47–83 (1973). ibid. 261 (1973), 29–54
Beauville, A.: Complex Algebraic Surfaces. London Mathematical Society Student Texts, vol. 34, 2nd edn. Cambridge University Press, Cambridge (1996)
Campillo, A.: Algebroid Curves in Positive Characteristic. Lecture Notes in Mathematics, vol. 613. Springer, Berlin (1980)
[+]
Abhyankar, S.S., Moh, T.T.: Newton-Puiseux expansion and generalized Tschirnhausen transformation. I, II. J. Reine Angew. Math. 260, 47–83 (1973). ibid. 261 (1973), 29–54
Beauville, A.: Complex Algebraic Surfaces. London Mathematical Society Student Texts, vol. 34, 2nd edn. Cambridge University Press, Cambridge (1996)
Campillo, A.: Algebroid Curves in Positive Characteristic. Lecture Notes in Mathematics, vol. 613. Springer, Berlin (1980)
Campillo, A., Piltant, O., Reguera, A.: Curves and divisors on surfaces associated to plane curves with one place at infinity. Proc. Lond. Math. Soc. 84, 559–580 (2002)
Casas-Alvero, E.: Singularities of Plane Curves. London Mathematical Society Lecture Note Series, vol. 276. Cambridge University Press, Cambridge (2000)
Ciliberto, C., Farnik, M., Küronya, A., Lozovanu, V., Roé, J., Shramov, C.: Newton–Okounkov bodies sprouting on the valuative tree. Rend. Circ. Mat. Palermo 2(66), 161–194 (2017)
Cutkosky, S.D., Ein, L., Lazarsfeld, R.: Positivity and complexity of ideal sheaves. Math. Ann. 321(2), 213–234 (2001)
de la Rosa-Navarro, B.L., Frías-Medina, J.B., Lahyane, M.: Rational surfaces with finitely generated Cox rings and very high Picard numbers. RACSAM 111, 297–306 (2017)
Delgado, F., Galindo, C., Núñez, A.: Saturation for valuations on two-dimensional regular local rings. Math. Z. 234, 519–550 (2000)
Demailly, J.P.: Singular Hermitian metrics on positive line bundles. Complex Algebraic Varieties (Bayreuth, 1990). Lecture Notes in Mathematics, vol. 1507, pp. 87–104. Springer, Berlin (1992)
Dumnicki, M., Harbourne, B., Küronya, A., Roé, J., Szemberg, T.: Very general monomial valuations of $$\mathbb{P}^2$$ and a Nagata type conjecture. Commun. Anal. Geom. 25, 125–161 (2017)
Favre, C., Jonsson, M.: The Valuative Tree. Lecture Notes in Mathematics, vol. 1853. Springer, Berlin (2004)
Favre, C., Jonsson, M.: Eigenvaluations. Ann. Sci. Éc. Norm. Sup. 40, 309–349 (2007)
Favre, C., Jonsson, M.: Dynamical compactifications of $$\mathbb{C}^2$$. Ann. Math. 173, 211–248 (2011)
Fulton, W.: Introduction to Toric Varieties. Annals of Mathematics Studies, vol. 131. Princeton University Press, Princeton (1993)
Galindo, C., Monserrat, F.: The cone of curves and the Cox ring of rational surfaces given by divisorial valuations. Adv. Math. 290, 1040–1061 (2016)
Galindo, C., Monserrat, F., Moyano-Fernández, J.: Minimal plane valuations. J. Algebraic Geom. 27, 751–783 (2018)
Galindo, C., Monserrat, F., Moyano-Fernández, J., Nickel, M.: Newton-Okounkov bodies of exceptional curve valuations. arXiv:1705.03948 (2017)
Greco, S., Kiyek, K.: General elements of complete ideals and valuations centered at a two-dimensional regular local ring. In: Christensen, C., Sathaye, A., Sundaram, G., Bajaj, C. (eds.) Algebra, Arithmetic and Geometry with Applications (West Lafayette, IN, 2000), pp. 381–455. Springer, Berlin (2004)
Hartshorne, R.: Algebraic Geometry. Graduate Texts in Mathematics, vol. 52. Springer, New York (1977)
Iitaka, S.: On $$D$$-dimensions of algebraic varieties. J. Math. Soc. Jpn. 23, 356–373 (1971)
Jonsson, M.: Dynamics on Berkovich Spaces in Low Dimensions. Springer, Berlin (2015)
Kaveh, K., Khovanskii, A.: Newton–Okounkov bodies, semigroups of integral points, graded algebras and intersection theory. Ann. Math. 176, 925–978 (2012)
Kollar, J., Mori, S.: Birational Geometry of Algebraic Varieties. Cambridge Tracts in Mathematics, vol. 134. Cambridge University Press, Cambridge (1998)
Moe, T.K.: Cuspidal curves on Hirzebruch surfaces. PhD thesis, Department of Mathematics, University of Oslo. https://www.duo.uio.no/handle/10852/37197 (2013). Accessed 23 Nov 2018
Mondal, P.: How to determine the sign of a valuation on $$\mathbb{C}[x, y]$$. Mich. Math. J. 66, 227–244 (2017)
Okounkov, A.: Why would multiplicities be log-concave? In: Duval, C., Ovsienko, V., Guieu, L. (eds.) The Orbit Method in Geometry and Physics (Marseille, 2000). Progress in Mathematics, vol. 213. Birkhäuser, Boston (2003)
Reid, M.: Chapters on algebraic surfaces. In: Kollár, J. (ed.) Complex Algebraic Geometry (Park city, UT, 1993). IAS/Park City Lecture Notes Series, vol. 3, pp. 3–159. American Mathematical Society, Providence (1997)
Spivakovsky, M.: Valuations in function fields of surfaces. Am. J. Math. 112, 107–156 (1990)
Teissier, B.: Valuations, deformations, and toric geometry. In: Kuhlmann, F.-Z., Kuhlmann, S., Marshall, M. (eds.) Valuation Theory and Its Applications, II (Saskatoon, SK, 1999). Fields Institute Communications, vol. 333. American Mathematical Society, Providence (1999)
Zariski, O., Samuel, P.: Commutative Algebra II. Vol. II. Graduate Texts in Mathematics, vol. 29. Springer, Berlin (1975)
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