K. Altmann and J. Hausen, Polyhedral divisors and algebraic torus actions, Mathematische Annalen, vol.334, issue.3, pp.557-607, 2006.
DOI : 10.1007/s00208-005-0705-8
URL : http://arxiv.org/abs/math/0306285

K. Altmann, J. Hausen, and H. Süss, Gluing Affine Torus Actions Via Divisorial Fans, Transformation Groups, vol.14, issue.64, pp.215-242, 2008.
DOI : 10.1007/s00031-008-9011-3
URL : http://arxiv.org/abs/math/0606772

M. Artin, On Isolated Rational Singularities of Surfaces, American Journal of Mathematics, vol.88, issue.1, pp.129-136, 1966.
DOI : 10.2307/2373050

A. Borel, Linear algebraic groups, Graduate Texts in Mathematics, vol.126, 1991.

D. Cox, J. Little, and H. Schenck, Toric varieties, Availiavle at

D. I. Dais, Resolving 3-dimensional toric singularities, Geometry of toric varieties, Sémin. Congr, vol.6, pp.155-186, 2002.

V. I. Danilov, The geometry of toric varieties, Uspekhi Mat, Nauk, vol.33, issue.247, pp.85-134, 0200.

[. Demazure, Sous-groupes alg??briques de rang maximum du groupe de Cremona, Annales scientifiques de l'??cole normale sup??rieure, vol.3, issue.4, pp.507-588, 1970.
DOI : 10.24033/asens.1201

M. Demazure, Anneaux gradués normaux, IntroductionàIntroductionà la théorie des singularités, II, Travaux en Cours, pp.35-68, 1988.

D. Daigle and G. Freudenburg, A Counterexample to Hilbert's Fourteenth Problem in Dimension 5, Journal of Algebra, vol.221, issue.2, pp.528-535, 1999.
DOI : 10.1006/jabr.1999.7987

I. V. Dolgachev, Automorphic forms and quasihomogeneous singularities, Functional Analysis and Its Applications, vol.93, issue.2, pp.67-68, 1975.
DOI : 10.1007/BF01075455

A. Dubouloz, The cylinder over the Koras-Russell cubic threefold has a trivial Makar-Limanov invariant, Transform, pp.531-539, 2009.

R. Elkik, Singularites rationnelles et deformations, Inventiones Mathematicae, vol.209, issue.2, pp.139-147, 1978.
DOI : 10.1007/BF01578068

G. Ewald, Combinatorial convexity and algebraic geometry, Graduate Texts in Mathematics, vol.168, 1996.
DOI : 10.1007/978-1-4612-4044-0

K. Fieseler and L. Kaup, Hyperbolic C * -actions on affine algebraic surfaces, Complex analysis, pp.160-168, 1991.

H. Flenner, S. Kaliman, and M. Zaidenberg, Completions of C * -surfaces, Affine algebraic geometry, pp.149-201, 2007.

G. Freudenburg, A counterexample to Hilbert's Fourteenth Problem in dimension six, Transformation Groups, vol.78, issue.1, pp.61-71, 2000.
DOI : 10.1007/BF01237178

G. Freudenburg, Algebraic theory of locally nilpotent derivations., Encyclopaedia of Mathematical Sciences 136. Invariant Theory and Algebraic Transformation Groups 7, 2006.

W. Fulton, Introduction to toric varieties, Annals of Mathematics Studies, vol.131, 1993.
DOI : 10.1515/9781400882526

H. Flenner and M. Zaidenberg, Normal affine surfaces with C * -actions, Osaka J. Math, vol.40, issue.4, pp.981-1009, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00323532

R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, 1977.

J. E. Humphreys, Linear algebraic groups, Graduate Texts in Mathematics, vol.21, issue.21, 1975.
DOI : 10.1007/978-1-4684-9443-3

S. Kaliman and L. Makar-limanov, On the Russell-Koras contractible threefolds, J. Algebraic Geom, vol.6, issue.2, pp.247-268, 1997.

J. Sándor and . Kovács, Du Bois singularities: on the conjectures of Kollár and Steenbrink, Compositio Math, vol.118, issue.2, pp.123-133, 1999.

T. Kambayashi and P. Russell, On linearizing algebraic torus actions, Journal of Pure and Applied Algebra, vol.23, issue.3, pp.243-250, 1982.
DOI : 10.1016/0022-4049(82)90100-1

S. Kuroda, A condition for finite generation of the kernel of a derivation, Journal of Algebra, vol.262, issue.2, pp.391-400, 2003.
DOI : 10.1016/S0021-8693(03)00067-X

H. B. Laufer, On Minimally Elliptic Singularities, American Journal of Mathematics, vol.99, issue.6, pp.1257-1295, 1977.
DOI : 10.2307/2374025

R. Lazarsfeld, Positivity in algebraic geometry. I, A Series of Modern, 2004.

A. Liendo and H. Süss, Normal singularities with torus actions, Tohoku Mathematical Journal, vol.65, issue.1, p.23, 2010.
DOI : 10.2748/tmj/1365452628
URL : https://hal.archives-ouvertes.fr/hal-00483304

D. Mumford, J. Fogarty, and F. Kirwan, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas, 1994.

[. Makar-limanov, Locally nilpotent derivations, a new ring invariant and applications

K. Miyake and T. Oda, Almost homogeneous algebraic varieties under algebraic torus action, Proc. Internat . Conf., Tokyo, pp.373-381, 1973.

M. Nagata, On the 14-th Problem of Hilbert, American Journal of Mathematics, vol.81, issue.3, pp.766-772, 1959.
DOI : 10.2307/2372927

T. Oda, Convex bodies and algebraic geometry. an introduction to the theory of toric varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete, 1988.
DOI : 10.1007/978-3-642-72547-0
URL : http://gdz.sub.uni-goettingen.de/download/PPN37915000X/PPN37915000X___LOG_0001.pdf

H. Pinkham, Normal surface singularities withC* action, Mathematische Annalen, vol.193, issue.2, pp.183-193, 1977.
DOI : 10.1007/BF01350195
URL : http://www.digizeitschriften.de/download/PPN235181684_0227/PPN235181684_0227___log34.pdf

L. Vladimir and . Popov, On the makar-limanov, derksen invariants , and finite automorphism groups of algebraic varieties, p.22, 2010.

L. Petersen and H. Süss, Torus invariant divisors, Israel Journal of Mathematics, vol.5, issue.1, p.13, 2008.
DOI : 10.1007/s11856-011-0039-z

R. Rentschler, Opérations du groupe additif sur le plan affine, C. R. Acad. Sci. Paris Sér. A-B, vol.267, pp.384-387, 1968.

P. Roberts, An infinitely generated symbolic blow-up in a power series ring and a new counterexample to Hilbert's fourteenth problem, Journal of Algebra, vol.132, issue.2, pp.461-473, 1990.
DOI : 10.1016/0021-8693(90)90141-A

I. Satake, On the arithmetic of tube domains (blowing-up of the point at infinity), Bull. Amer, Math. Soc, pp.79-1076, 1973.

H. Süss, Canonical divisors on T-varieties, arXiv:0811.0626v1 [math, 2008.

D. A. Timashev, Classification of $G$-varieties of complexity 1, Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, vol.61, issue.2, pp.127-162, 1997.
DOI : 10.4213/im119

D. Timashev, Torus actions of complexity one, Contemp. Math. Amer. Math. Soc, vol.460, pp.349-364, 2008.
DOI : 10.1090/conm/460/09029

R. Vollmert, Toroidal embeddings and polyhedral divisors, p.5, 2007.

K. Watanabe, On plurigenera of normal isolated singularities. I, Math, Ann, vol.250, issue.1, pp.65-94, 1980.

K. Watanabe, Some remarks concerning Demazure???s construction of normal graded rings, Nagoya Mathematical Journal, vol.146, pp.203-211, 1981.
DOI : 10.1007/BF01350195

S. Shing and T. Yau, On maximally elliptic singularities, Trans. Amer. Math. Soc, vol.257, issue.2, pp.269-329, 1980.