Access the full text.
Sign up today, get DeepDyve free for 14 days.
M. Zaidenberg (1988)
Isotrivial Families of Curves on Affine Surfaces and Characterization of the Affine PlaneMathematics of The Ussr-izvestiya, 30
W. Vasconcelos (1969)
Derivations of commutative noetherian ringsMathematische Zeitschrift, 112
(1982)
Topol ogie dessurfacescom pl exescom pactessingul i eres,i n:Surl a topol ogie des surfaces com pl exes com pactes
J. Kollár (1992)
Flips and Abundance for Algebraic ThreefoldsAstérisque, 211
N A 2/72, U niversit atsstr.150,44780 B ochum
H. Kraft, C. Procesi (1982)
On the geometry of conjugacy classes in classical groupsCommentarii Mathematici Helvetici, 57
(1974)
237{244. [ C l G r] C . H . C l em ens
A. Seidenberg (1966)
Derivations and integral closurePacific Journal of Mathematics, 16
Kei-ichi Watanabe (1974)
Certain invariant subrings are Gorenstein. IIOsaka Journal of Mathematics, 11
Henry Laufer (1971)
Normal Two-Dimensional Singularities.
K. Masuda, M. Miyanishi (2001)
Étale endomorphisms of algebraic surfaces with $G_m$-actionsMathematische Annalen, 319
H. Pinkham (1977)
Normal surface singularities withC* actionMathematische Annalen, 227
Hubert Flenner (1981)
Rationale quasihomogene SingularitätenArchiv der Mathematik, 36
(1995)
O n singul arities thatare quasirationalin the sense ofA bhyankar,U spekhiM at
M. Gizatullin, V. Danilov (1975)
AUTOMORPHISMS OF AFFINE SURFACES. IMathematics of The Ussr-izvestiya, 9
(1973)
S]G .K em pf,F.K nudsen,D.M um ford,B.Saint-Donat,Toroidalem beddings,Lecture Notes in M athem atics339,Springer-Verlag,Berlin-Heidelberg-New York,1973
F. Beukers (1998)
The Diophantine equation $Ax^p+By^q=Cz^r$Duke Mathematical Journal, 91
J. Kollár (1986)
Higher direct images of dualizing sheaves. IIAnnals of Mathematics, 124
Y. Miyaoka (1995)
Rational Curves on Algebraic Varieties
Sur l a reduction des equations di erentiell es l in eaires aux form es int egrabl es, M em oi respr esent espardi verssavants a l ' A cadem i e dessci encesde l ' Insti tutN ati onalde France
M. Morales (1987)
Resolution of quasi-homogeneous singularities and plurigeneraCompositio Mathematica, 64
W. Brownawell, D. Masser (1986)
Vanishing sums in function fieldsMathematical Proceedings of the Cambridge Philosophical Society, 100
(1996)
O n the hypersurface x + x 2 y+ z 2 + t 3 = 0 in C 4 or a C 3 -l ike threefol d which is notC 3
J. Bertin (1983)
Pinceaux de droites et automorphismes des surfaces affines.Journal für die reine und angewandte Mathematik (Crelles Journal), 1983
G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat (1973)
Toroidal Embeddings I
Martin d'H` eres cédex, France E-mail address: zaidenbe@ujf-grenoble
J. Wahl (1977)
Equations defining rational singularitiesAnnales Scientifiques De L Ecole Normale Superieure, 10
S. Kaliman, M. Zaidenberg (2000)
Miyanishi's characterization of the affine 3-space does not hold in higher dimensionsAnnales de l'Institut Fourier, 50
S. Goto, Kei-ichi Watanabe (1978)
On graded rings, IJournal of The Mathematical Society of Japan, 30
E. Brieskorn (1968)
Rationale Singularitäten komplexer FlächenInventiones mathematicae, 4
Y. Kawamata (1988)
Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfacesAnnals of Mathematics, 127
H. Clemens, P. Griffiths (1972)
The intermediate Jacobian of the cubic threefoldAnnals of Mathematics, 95
(1989)
Remarks on the topology of surface singularities and applications. With an appendix by K. Paranjape
E. Viehweg (1977)
Rational singularities of higher dimensional schemes, 63
F. Sakai (1977)
Complex Analysis and Algebraic Geometry: Kodaira Dimensions of Complements of Divisors
H. Grauert, O. Riemenschneider (1970)
Verschwindungssätze für analytische Kohomologiegruppen auf komplexen RäumenInventiones mathematicae, 11
(1971)
Pri nceton U ni versi ty Press and U ni versi ty ofTokyo Press.X I,161 p. [ La 2 ] H .B .Laufer,O n rationalsingul arities,A m er
H. Schwarz
Ueber diejenigen Fälle, in welchen die Gaussische hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt.Journal für die reine und angewandte Mathematik (Crelles Journal), 1873
(1984)
Ergebni sse der M athem ati k und i hrer G renzgebi ete (3),Spri nger-Verl ag
(1994)
On the equations z^m = F(x,y) and Ax^p + By^q = Cz^r
(1980)
Singul arit es de K l ein| I,II,S em i nai re surl esSi ngul ari t esdesSurfaces(C entre de M ath em ati quesde l ' Ecol e Pol ytechni que
(1967)
On n-dimensional compact complex varieties with n algebraically independent meromorphic functions. I-III, Amer
F. Baldassari, B. Dwork (1979)
On Second Order Linear Differential Equations with Algebraic SolutionsAmerican Journal of Mathematics, 101
D. Burns (1974)
On rational singularities in dimensions > 2Mathematische Annalen, 211
Hubert Flenner (1981)
Divisorenklassengruppen quasihomogener Singularitäten.Journal für die reine und angewandte Mathematik (Crelles Journal), 1981
H. Flenner, M. Zaidenberg (2000)
Log–canonical forms and log canonical singularitiesMathematische Nachrichten, 254-255
(1968)
Vanishing sum s in function el ds, M ath. Proc.C am bri dge Phi l os
(1999)
Joins and intersections,Spri nger Verl ag,B erl i n{H ei del berg{N ew York
A. Moriwaki (1987)
Torsion freeness of higher direct images of canonical bundlesMathematische Annalen, 276
R. Mason (1984)
Diophantine Equations Over Function Fields
M. Saito (1988)
Modules de Hodge PolarisablesPublications of The Research Institute for Mathematical Sciences, 24
M. Artin (1966)
ON ISOLATED RATIONAL SINGULARITIES OF SURFACES.American Journal of Mathematics, 88
(1980)
Pol ynom ial sol utions of F (x;y) = z n , Proceedi ngs of the Q ueen' s N um ber T heory C onference,1979 (K i ngston,O nt. ,1979),Q ueen' s Papers i n Pure and A ppl .M ath.54, Q ueen' s U ni v
(2001)
Lecture Notes in Mathematics
(1971)
form erl y A .G utw i rth),O n pol ynom ialequations
D. Arapura (1986)
A note on Kollár’s theoremDuke Mathematical Journal, 53
(1981)
Journal reine angew. Math
W. Barth (2003)
Compact complex surfaces.
S Stepanov (1981)
Diophantine equations over function fieldsMathematical notes of the Academy of Sciences of the USSR, 32
M. Miyanishi (1981)
Singularities of normal affine surfaces containing cylinderlike open setsJournal of Algebra, 68
T. Tomaru, H. Saito, T. Higuchi (1981)
Pluri-Genera δ_m of Normal Surface Singularities with C^*-Action, 28
(1968)
Opérations du groupe additif sur le plane affine
酒井 文雄 (1977)
Kodaira dimensions of complements of divisors = 因子の補集合の小平次元
NA 2/72, Universitätsstr . 150, 44780 Bochum, Germany E-mail address: Hubert.Flenner@ruhr-uni-bochum
Kimio Watanabe (1980)
On plurigenera of normal isolated singularities. IMathematische Annalen, 250
(1995)
Rational curves on al gebraic varieties, Ergebni sse der M athem ati k 32, Spri nger-Verl ag,B erl i n
(1983)
A utom orphism es des surfaces non com pl etes,groupes Fuchsiens etsingul arit es quasihom og enes,S em i n.d' al g ebre P.D ubrei let M
P. Orlik, P. Wagreich (1972)
Equivariant resolution of singularities with C* action
We study rational curves on algebraic varieties, especially on normal affine varieties endowed with a ℂ*-action. For varieties with an isolated singularity, covered by a family of rational curves with a general member not passing through the singular point, we show that this singularity is rational. In particular, this provides an explanation of classical results due to H. A. Schwartz and G. H. Halphen on polynomial solutions of the generalized Fermat equation.
Mathematische Zeitschrift – Springer Journals
Published: Jul 1, 2003
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.