Nous présentons un exemple qui confirme l’assertion du titre.
We present an example which confirms the assertion of the title.
@article{AIF_2000__50_6_1649_0, author = {Kaliman, Shulim and Zaidenberg, Mikhail}, title = {Miyanishi's characterization of the affine 3-space does not hold in higher dimensions}, journal = {Annales de l'Institut Fourier}, pages = {1649--1669}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {50}, number = {6}, year = {2000}, doi = {10.5802/aif.1803}, mrnumber = {2002c:14094}, zbl = {0971.14044}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1803/} }
TY - JOUR AU - Kaliman, Shulim AU - Zaidenberg, Mikhail TI - Miyanishi's characterization of the affine 3-space does not hold in higher dimensions JO - Annales de l'Institut Fourier PY - 2000 SP - 1649 EP - 1669 VL - 50 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1803/ DO - 10.5802/aif.1803 LA - en ID - AIF_2000__50_6_1649_0 ER -
%0 Journal Article %A Kaliman, Shulim %A Zaidenberg, Mikhail %T Miyanishi's characterization of the affine 3-space does not hold in higher dimensions %J Annales de l'Institut Fourier %D 2000 %P 1649-1669 %V 50 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1803/ %R 10.5802/aif.1803 %G en %F AIF_2000__50_6_1649_0
Kaliman, Shulim; Zaidenberg, Mikhail. Miyanishi's characterization of the affine 3-space does not hold in higher dimensions. Annales de l'Institut Fourier, Tome 50 (2000) no. 6, pp. 1649-1669. doi : 10.5802/aif.1803. http://www.numdam.org/articles/10.5802/aif.1803/
[Ab] Quasirational singularities, Amer. J. Math., 101-2 (1979), 267-300. | MR | Zbl
,[BaDw] On second order linear differential equations with algebraic solutions, Amer. J. Math., 101 (1979), 42-76. | MR | Zbl
, ,[BarKa] Topologie des surfaces complexes compactes singulières, in: Sur la topologie des surfaces complexes compactes, Sém. Math. Sup., 80, Presses Univ. Montréal, Montréal, Que. (1982), 61-297. | MR | Zbl
, ,[Be] Automorphismes des surfaces non complètes, groupes fuchsiens et singularités quasihomogènes, Sémin. d'algèbre P. Dubreil et M.-P. Malliavin, 36ème Année, Proc., Paris 1983/84, Lect. Notes Math., 1146 (1985), 106-126. | MR | Zbl
,[Beu] The Diophantine equation Axp + Byq = Czr, Duke Math. J., 91-1 (1998), 61-88. | MR | Zbl
,[Bu] The abc theorem for abelian varieties, Intern. Math. Res. Notices, 5 (1994), 219-232. | MR | Zbl
,[BoMu] Trinomial equations in function fields, Astérisque, 22 (1995), 19-40. | MR | Zbl
, ,[Br] On the equation F(x,y) = zm over function fields, Acta Math. Hung., 49 (1987), 267-275. | MR | Zbl
,[ClGr] The intermediate Jacobian of the cubic threefold, Ann. of Math., 95 (1972), 281-356. | MR | Zbl
, ,[DanGi] Automorphisms of affine surfaces. I, II, Math. USSR Izv., 9 (1975), 493-534; ibid., 11 (1977), 51-98. | Zbl
, ,[DarGr] On the equations zm = F(x,y) and Axp + Byq = Czr, Bull. London Math. Soc., 27 (1995), 513-543. | Zbl
, ,[Dav] On f3(t) - g2(t), Norske Vid. Selsk. Forh. (Trondheim), 38 (1965), 86-87. | Zbl
,[De] Constructive Invariant Theory and the Linearization Problem, Ph. D. thesis, Basel (1997), 39p. | MR | Zbl
,[tDP] Contractible affine surfaces of Kodaira dimension one, Japan J. Math., 16 (1990), 147-169. | MR | Zbl
, ,[DvZa] A note on Thue's equation over function fields, Monatsh. für Math., 118 (1994), 219-230. | MR | Zbl
, ,[Ev] On polynomial equations, Israel J. Math., 10 (1971), 321-326. | Zbl
(formely ),[FIZa] Rational curves and rational singularities, in preparation.
, ,[Fu] On the topology of non complete algebraic surfaces, J. Fac. Sci. Univ. Tokyo, Sect. IA, 29 (1982), 503-566. | MR | Zbl
,[Grm] Oka's principle for holomorphic sections of elliptic bundles, J. Amer. Math. Soc., 2 (1989), 851-897. | MR | Zbl
,[Grs] On the functional equation fn + gn = hn, Amer. Math. Monthly, 73 (1966), 1093-1096. | MR | Zbl
,[Ha] Sur la réduction des équations différentielles linéaires aux formes intégrables, Mémoires présentés par divers savants à l'Académie des sciences de l'Institut National de France, T. XXVIII, N 1, Paris, F. Krantz, 1883; uvres. Vol. 3, Paris (1921), 1-260.
,[Ja] Elementary proof of a theorem of P. Montel on entire functions, J. Lond. Math. Soc., 40 (1965), 166-170. | MR | Zbl
,[Ka1] Exotic analytic structures and Eisenman intrinsic measures, Israel Math. J., 88 (1994), 411-423. | MR | Zbl
,[Ka2] Polynomials with general ℂ2-fibers are variables.I, preprint (1999), 60p.
,[KaML1] On Russell-Koras contractible threefolds, J. of Algebraic Geom., 6 (1997), 247-268. | MR | Zbl
, ,[KaML2] Affine algebraic manifolds without dominant morphisms from Euclidean spaces, Rocky Mount. J. Math., 27-2 (1997), 601-609. | MR | Zbl
, ,[KaML3] Locally nilpotent derivations of Jacobian type, preprint (1998), 16p.
, ,[KaZa1] Affine modifications and affine varieties with a very transitive automorphism group, Transformation Groups, 4-1 (1999), 53-95. | MR | Zbl
, ,[KaZa2] Families of affine planes: the existence of a cylinder, MPI, preprint MPI 00-75 (2000), 12p.
, ,[KlNe] On the number of distinct zeros of polynomials, Amer. Mathem. Monthly, 66 (1959), 494-496. | MR | Zbl
, ,[Kl] Vorlesungen über das ikosaeder und die auflösung der gleichungen vom fünden grade, Teubner, Leipzig, 1884. English transl.: , Lectures on the Icosahedron and the solution of equations of fifth degree, Dover, 1956.
,[La] Old and new conjectured Diophantine inequalities, Bull. Amer. Math. Soc., 23 (1990), 37-75. | MR | Zbl
,[ML1] On the hypersurface x + x2y + z2 +t3 = 0 in ℂ4 or a ℂ3-like threefold which is not ℂ3, Israel J. Math., 96 (1996), 419-429. | MR | Zbl
,[ML2] On groups of automorphisms of a class of surfaces, Israel J. Math., 69 (1990), 250-256. | MR | Zbl
,[ML3] On the group of automorphisms of a surface xny = P(z), Preprint (1997), 11p.
,[Man] Cubic forms. Algebra, geometry, arithmetic, North-Holland Mathematical Library, 4. North-Holland Publishing Co., Amsterdam-New York (1986), 326 p. (The Russian original "Nauka", Moscow, 1972). | Zbl
,[Mas] Equations over function fields, Number theory, Noordwijkerhout 1983. Lecture Notes in Math., 1068, Springer, Berlin-New York (1984), 149-157. | MR | Zbl
,[Mil] On the 3-dimensional Brieskorn manifolds M(p, q, r), in: Knots, groups, and 3-manifolds, L. P. Neuwirth, ed. Annals of Math. Stud., Princenton Univ. Press, Princeton, NJ (1975), 175-225. | MR | Zbl
,[Miy] Algebraic characterization of the affine 3-space, Proc. Algebraic Geom. Seminar, Singapore, World Scientific (1987), 53-67.
,[Ore1] Riemann existence theorem and construction of real algebraic curves, preprint (1999), 1-11.
,[Ore2] On singularities that are quasirational in the sense of Abhyankar, Uspekhi Mat. Nauk, 50 (1995), no. 6 (306), 201-202. | MR | Zbl
,[OrlWa] Algebraic surfaces with k*-action, Acta Math., 138 (1977), 43-81. | MR | Zbl
, ,[PaVa] Sums of three cubes, The arithmetic of function fields (Columbus, OH, 1991), Ohio State Univ. Math. Res. Inst. Publ., 2, de Gruyter, Berlin (1992), 443-454. | MR | Zbl
, ,[Pr] Mnogochleny (Polynomials) (in Russian), MCNMO, Moscow, 2000.
,[Sa] Polynomial ring in two variables over a D. V. R.: A criterion, Invent. Math., 74 (1983), 159-168. | MR | Zbl
,[Sch] Polynomial solutions of F(x,y) = zn, Proceedings of the Queen's Number Theory Conference, 1979 (Kingston, Ont., 1979), Queen's Papers in Pure and Appl. Math., 54, Queen's Univ., Kingston, Ont. (1980), 33-65. | Zbl
,[Schw] Ueber diejenigen Fälle, in welchen die Gaussische hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt, J. für die reine und angewandte Mathematik, 75 (1873), 292-335. | JFM
,[Si] The S-unit equation over function fields, Math. Proc. Cambridge Philos. Soc., 95 (1984), 3-4. | MR | Zbl
,[St] Polynomial identities and Hauptmoduln, Quart. J. Math. (2), 32 (1981), 349-370. | MR | Zbl
,[Ve] On power values of binary forms over function fields, Publ. Math. Debrecen, 50-1, 2 (1997), 145-148. | MR | Zbl
,[Wi] On automorphisms of complements of analytic subsets in Cn, Math. Zeitschrift, 204 (1990), 117-127. | MR | Zbl
,[Za1] An analytic cancellation theorem and exotic algebraic structures on ℂn, n ≥ 3, Astérisque, 217 (1993), 251-282. | Zbl
,[Za2] On exotic algebraic structures on affine spaces, Algebra and Analysis. St. Petersbourg Mathem. J., 10-5 (1999), 60p.
,[Zn] On Davenport's bound for the degree of f3 - g2 and Riemann's existence theorem, Acta Arithm., 71 (1995), 107-137; Addenda, ibid., 74 (1996), 387. | MR | Zbl
,Cité par Sources :