MR 1423629 | Zbl 0892.14003 | 2 citations in Numdam

[AC95] N. A'Campo, M. Oka - Geometry of plane curves via Tschirnhausen resolution towers. J. Alg. Geometry (1995) (to appear). | Zbl 0904.14014

[AbM75] S. S. Abhyankar, T. T. Moh - Embeddings of the line in the plane. J. Reine Angew. Math. 276 (1975) 149-166. | MR 379502 | Zbl 0332.14004

[As94] T. Asanuma - Non-linearizable algebraic group actions on ${𝔸}^n$. J. Algebra 166 (1994) 72-79. | Article | Zbl 0817.14027

[Ba84] H. Bass - A non-triangular action of $G_a$ on ${𝔸}^3$. J. Pure Appl. Algebra 33 (1984) 1-5. | Article | MR 750225 | Zbl 0555.14019

[BaH85] H. Bass, W. Haboush - Linearizing certain reductive group actions. Trans. Amer. Math. Soc. 292 (1985) 463-482. | Article | MR 808732 | Zbl 0602.14047

[BaH87] H. Bass, W. Haboush - Some equivariant $K$-theory of affine algebraic group actions. Comm. Algebra 15 (1987) 181-217. | Article | MR 876977 | Zbl 0612.14047

[Bi66] A. Białynicki-Birula - Remarks on the action of an algebraic torus on $k^n$, I. Bull. Acad. Polon. Sci. Sér. Sci. Math. 14 (1966) 177-181. | Zbl 0163.42901

[Bi67] A. Białynicki-Birula - Remarks on the action of an algebraic torus on $k^n$, II. Bull. Acad. Polon. Sci. Sér. Sci. Math. 15 (1967) 123-125. | Zbl 0163.42901

[Bi76] A. Białynicki-Birula - Some properties of the decompositions of algebraic varieties determined by actions of a torus. Bull. Acad. Polon. Sci. Sér. Sci. Math. 24 (1976) 667-674. | Zbl 0355.14015

[CaL70] I. Canals, E. Lluis - Acerca de un resultado de Segre. Anales del Inst. de Metam., Univ. Nac. Aut. México 10 (1970) 1-15. | MR 286794 | Zbl 0234.14011

[Da89] W. Danielewski - On the cancellation problem and automorphism group of affine algebraic varieties. Preprint 1989. (Appendix by K. Fieseler)

[Di90] A. Dimca - Hypersurfaces in ${ℂ}^n$ diffeomorphic to ${ℝ}^{4n-2}$. Max-Planck Institut Bonn, preprint 1990.

[Di92] A. Dimca - Singularities and topology of hypersurfaces. Universitext, Springer Verlag, Berlin-Heidelberg-New York, 1992. | Article | MR 1194180 | Zbl 0753.57001

[DMP89] K.-H. Dovermann, M. Masuda, T. Petrie - Fixed point free algebraic actions on varieties diffeomorphic to ${ℝ}^n$. In: Topological methods in algebraic transformation groups (H. Kraft et al., eds.). Progress in Math. vol. 80, Birkhäuser Verlag, Basel - Boston, 1989, pp. 47-80. | MR 1040857 | Zbl 0695.57021

[EaH73] P. Eakin, W. Heinzer - A cancellation problem for rings. In: Conference on Commutative Algebra (Brewer, J.W.; Rutter, E.A., eds.). Lecture Notes in Mathematics vol. 311, Springer Verlag, Berlin-Heidelberg-New York, 1973, pp. 61-77. | Article | MR 349664 | Zbl 0271.13010

[Fa95] M. Fankhauser - Fixed points for reductive group actions on acyclic varieties. Ann. Inst. Fourier (1995) to appear. (Thesis Basel 1994) | Numdam | MR 1370747

[Fi94] K.-H. Fieseler - On complex affine surfaces with ${ℂ}^{+}$-action. Comment. Math. Helv. 69 (1994) 5-27. | Article | MR 1259603 | Zbl 0806.14033

[Fu79] T. Fujita - On Zariski problem. Proc. Japan Acad. Ser. A. Math. Sci. 55 (1979) 106-110. | Article | MR 531454 | Zbl 0444.14026

[Fu81] T. Fujita - Cancellation problem for complete varieties. Invent. Math. 64 (1981) 119-121. | Article | MR 621772 | Zbl 0462.14001

[Fu82] T. Fujita - On the topology of non-complete surfaces. J. Fac. Sci. Univ. Tokyo 29 (1982) 503-566. | MR 687591 | Zbl 0513.14018

[GiD75] M. H. Gizatullin, V. I. Danilov - Automorphisms of affine surfaces, I. Math. USSR-Izv. 9 (1975) 493-534. | Article | MR 376701 | Zbl 0331.14007

[Gu88] J. Gubeladze - Anderson's conjecture and the maximal monoid class over which projective modules are free. Math. USSR-Sb. 63 (1988) 165-180. | Article | MR 937805 | Zbl 0668.13011

[GuM87] R. V. Gurjar, M. Miyanishi - Affine surfaces with $\overline{\kappa }\le 1$. In: "Algebraic Geometry and Commutative Algebra" in Honor of Masayoshi Nagata., 1987, pp. 99-124. | Zbl 0707.14015

[GuM95] R. V. Gurjar, M. Miyanishi - On contractible curves in ${ℂ}^2$. Preprint 1995.

[HeK94] P. Heinzner, F. Kutzschebauch - An equivariant version of Grauert's Oka principle. Invent. Math. 119 (1994) 317-346. | Article | MR 1312503 | Zbl 0837.32004

[Ho72] M. Hochster - Nonuniqueness of coefficient rings in a polynomial ring. Proc. Amer. Math. Soc. 34 (1972) 81-82. | Article | MR 294325 | Zbl 0233.13012

[HsS86] W. Hsiang, E. Straume - Actions of compact connected Lie groups on acyclic manifolds with low dimensional orbit space. J. Reine Angew. Math. 369 (1986) 21-39. | MR 850627 | Zbl 0583.57025

[Ii82] S. Iitaka - Algebraic Geometry : An introduction to birational geometry of algebraic varieties. Graduate Texts in Mathematics, vol. 76, Springer Verlag, Berlin-Heidelberg-New York, 1982. | Article | MR 637060 | Zbl 0491.14006

[IiF77] S. Iitaka, T. Fujita - Cancellation theorem for algebraic varieties. J. Fac. Sci. Univ. Tokyo 24 (1977) 123-127. | MR 450278 | Zbl 0353.14013

[Je87] Z. Jelonek - The extension of regular and rational embeddings. Math. Ann. 113 (1987) 113-120. | Article | MR 884649 | Zbl 0611.14010

[Je91] Z. Jelonek - Identity sets for polynomial automorphisms. J. Pure Appl. Algebra 76 (1991) 333-339. | Article | MR 1147306 | Zbl 0752.14010

[Je92] Z. Jelonek - The Jacobian Conjecture and the extension of a polynomial embeddings. Math. Annalen 294 (1992) 289-293. | Article | MR 1183407 | Zbl 0757.14007

[Je93] Z. Jelonek - Irreducible identity sets for polynomial automorphisms. Math. Zeitschrift 212 (1993) 601-617. | Article | MR 1214049 | Zbl 0806.14011

[Je94] Z. Jelonek - Affine smooth varieties with finite group of automorphisms. Math. Zeitschrift 216 (1994) 575-591. | Article | MR 1288046 | Zbl 0824.14012

[Ju42] H. W. E. Jung - Über ganze birationale Transformationen der Ebene. J. Reine Angew. Math. 184 (1942) 161-174. | JFM 68.0382.01 | MR 8915

[Ka91] S. Kaliman - Extensions of isomorphisms between affine algebraic subvarieties of $k^n$ to automorphisms of $k^n$. Proc. Amer. Math. Soc. 113 (1991) 325-334. | MR 1076575 | Zbl 0743.14011

[Ka93] S. Kaliman - Smooth contractible hypersurfaces in ${ℂ}^n$ and exotic algebraic structures on ${ℂ}^3$. Math. Zeitschrift 214 (1993) 499-510. | Article | MR 1245209 | Zbl 0792.57013

[Ka95] S. Kaliman - Exotic structures on ${ℂ}^n$ and ${ℂ}^{*}$-actions on ${ℂ}^3$. In: Proceedings on "Complex Analysis and Geometry". Lecture Notes in Pure and Appl. Math., Marcel Dekker Inc., 1995 (to appear) | MR 1365979 | Zbl 0870.58007

[KaM95a] S. Kaliman, L. Makar-Limanov - Affine algebraic manifolds without dominant morphisms from euclidean space. Preprint 1995. | MR 1466159 | Zbl 0951.14007

[KaM95b] S. Kaliman, L. Makar-Limanov - On Russell's contractible threefolds. Preprint 1995.

[Kam75] T. Kambayashi - On the absence of nontrivial separable forms of the affine plane. J. Algebra 35 (1975) 449-456. | Article | MR 369380 | Zbl 0309.14029

[Kam79] T. Kambayashi - Automorphism group of a polynomial ring and algebraic group action on an affine space. J. Algebra 60 (1979) 439-451. | Article | MR 549939 | Zbl 0429.14017

[Kam80] T. Kambayashi - On Fujita's strong cancellation theorem for the affine plane. J. Fac. Sci. Univ. Tokyo, Sec. IA 27 (1980) 535-548. | MR 603951 | Zbl 0453.14015

[KaR82] T. Kambayashi, P. Russell - On linearizing algebraic torus actions. J. Pure Appl. Algebra 23 (1982) 243-250. | Article | MR 644276 | Zbl 0518.14026

[Kn91] F. Knop - Nichtlinearisierbare Operationen halbeinfacher Gruppen auf affinen Räumen. Invent. Math. 105 (1991) 217-220. | Article | MR 1109627 | Zbl 0739.20019

[KoR86] M. Koras, P. Russell - $G_m$-actions on ${𝔸}^3$. In: Canad. Math. Soc. Confer. Proc.. vol. 6, 1986, pp. 269-276. | MR 846023 | Zbl 0591.14034

[KoR89a] M. Koras, P. Russell - Codimension $2$ torus actions on affine $n$-space. In: Canad. Math. Soc. Confer. Proc.. Proceedings of the Conference on "Group Actions and Invariant Theory", Montreal 1988 vol. 10, 1989, pp. 103-110. | MR 1021282 | Zbl 0725.14036

[KoR89b] M. Koras, P. Russell - On linearizing "good" ${ℂ}^{*}$-actions on ${ℂ}^3$. In: Canad. Math. Soc. Confer. Proc.. Proceedings of the Conference on "Group Actions and Invariant Theory" , Montreal 1988 vol. 10, 1989, pp. 93-102. | MR 1021281 | Zbl 0687.14037

[KoR95] M. Koras, P. Russell - Contractible algebraic threefolds and ${ℂ}^{*}$-actions on ${ℂ}^3$. Preprint 1995. | Zbl 0882.14013

[Kr89a] H. Kraft - Algebraic automorphisms of affine space. In: Topological methods in algebraic transformation groups (H. Kraft et al., eds.). Progress in Math. vol. 80, Birkhäuser Verlag, Basel-Boston, 1989, pp. 81-105. | MR 1040858 | Zbl 0719.14030

[Kr89b] H. Kraft - $G$-vector bundles and the linearization problem. In: Proceedings of the Conference on "Group Actions and Invariant Theory" , Montreal 1988. Can. Math. Soc. Conf. Proc. vol. 10, 1989, pp. 111-123. | MR 1021283 | Zbl 0703.14009

[Kr90] H. Kraft - ${ℂ}^{*}$-actions on affine space. In: Operator Algebras, Unitary Representations, Envelopping Algebras, and Invariant Theory (A. Connes, M. Duflo, A. Joseph, R. Rentschler, eds.). Progress in Mathematics vol. 92, Birkhäuser Verlag, Basel-Boston, 1990, pp. 561-579. | MR 1103604 | Zbl 0747.14014

[KrP85] H. Kraft, V. L. Popov - Semisimple group actions on the three dimensional affine space are linear. Comment. Math. Helv. 60 (1985) 466-479. | Article | MR 814152 | Zbl 0645.14020

[KrS89] H. Kraft, G. W. Schwarz - Linearizing reductive group actions on affine space with one-dimensional quotient. In: Proceedings of the Conference on "Group Actions and Invariant Theory," Montreal 1988. Contemp. Math. vol. 10, 1989 | MR 1021284 | Zbl 0704.14039

[KrS92] H. Kraft, G. W. Schwarz - Reductive group actions with one-dimensional quotient. Publ. Math. IHES 76 (1992) 1-97. | Article | Numdam | MR 1215592 | Zbl 0783.14026

[KrS95] H. Kraft, G. W. Schwarz - Finite automorphisms of affine $n$-space. In: Proceedings of the Curaçao Conference on "Automorphisms of Affine Space". to appear, 1995 | Article | MR 1352703 | Zbl 0837.14010

[Li77] A. Libgober - A geometrical procedure for killing the middle dimensional homology groups of algebraic hypersurfaces. Proc. Amer. Math. Soc. 63 (1977) 198-202. | Article | MR 440576 | Zbl 0359.14007

[Lu73] D. Luna - Slices étales. Bull. Soc. Math. France, Mémoire 33 (1973) 81-105. | Article | Numdam | MR 342523 | Zbl 0286.14014

[Ma94] L. Makar-Limanov - On the hypersurface $x+x^{2}y+z^2+t^3=0$ in ${ℂ}^4$. Preprint 1994. | MR 1289046

[MMP91] M. Masuda, L. Moser-Jauslin, T. Petrie - Equivariant algebraic vector bundles over representations of reductive groups: Applications. Proc. Natl. Acad. Sci. USA 88 (1991) 9065-9066. | Article | MR 1129885 | Zbl 0753.14005

[MMP95] M. Masuda, L. Moser-Jauslin, T. Petrie - The equivariant Serre Problem for abelian groups. J. Amer. Math. Soc (1995). | MR 1380501 | Zbl 0884.14007

[MaP91] M. Masuda, T. Petrie - Equivariant algebraic vector bundles over representations of reductive groups: Theory. Proc. Natl. Acad. Sci. USA 88 (1991) 9061-9064. | MR 1129884 | Zbl 0753.14042

[Me95] K. Mederer - Moduli of equivariant $G$-vector bundles. Thesis Brandeis 1995.

[Mi87] M. Miyanishi - Algebraic characterization of the affine 3-space. Proc. Alg. Geometry Seminar, Singapore, World Scientific, 1987, pp. 53-67. | MR 966444

[MiS80] M. Miyanishi, T. Sugie - Affine surfaces containing cylinderlike open sets. J. Math. Kyoto Univ. 20 (1980) 11-42. | Article | MR 564667 | Zbl 0445.14017

[MiT87] M. Miyanishi, S. Tsunoda - Open algebraic surfaces with Kodaira dimension -$\infty$. Proc. Sympos. Pure Math. 46 (1987) 435-450. | Article | Zbl 0643.14021

[Na67] M. Nagata - A theorem on valuation rings and its applications. Nagoya Math. J. 29 (1967) 85-91. | Article | MR 207688 | Zbl 0146.26302

[Ne89a] W. D. Neumann - On the topology of curves in complex surfaces. In: Topological methods in algebraic transformation groups (H. Kraft et al, eds.). Progress in Math. vol. 80, Birkhäuser Verlag, Basel-Boston, 1989, pp. 117-133. | MR 1040860 | Zbl 0715.14025

[Ne89b] W. D. Neumann - Complex algebraic plane curves via their links at infinity. Invent. math. 98 (1989) 445-489. | Article | MR 1022302 | Zbl 0734.57011

[Pa84] D. I. Panyushev - Semisimple automorphism groups of four-dimensional affine space. Math. USSR-Izv. 23 (1984) 171-183. | Article | Zbl 0581.14033

[PeR86] T. Petrie, J. D. Randall - Finite-order algebraic automorphisms of affine varieties. Comment. Math. Helv. 61 (1986) 203-221. | Article | MR 856087 | Zbl 0612.14046

[Ra71] C. P. Ramanujam - A topological characterization of the affine plane as an algebraic variety. Ann. of Math. 94 (1971) 69-88. | Article | MR 286801 | Zbl 0218.14021

[Re68] R. Rentschler - Opérations du groupe additif sur le plan affine. C. R. Acad. Sci. Paris 267 A (1968) 384-387. | MR 232770 | Zbl 0165.05402

[Rud82] L. Rudolph - Embedding of the line in the plane. J. Reine Angew. Math. 337 (1982) 113-118. | MR 676044 | Zbl 0486.14003

[Ru81] P. Russell - On affine-ruled rational surfaces. Math. Ann. 255 (1981) 287-302. | Article | MR 615851 | Zbl 0438.14024

[Ru92] P. Russell - On a class of ${ℂ}^3$-like threefolds. Preliminary report 1992.

[Ru95] P. Russell - Open problems on open algebraic varieties (Montreal 1994 Problems). Prépublication de l'Institut Fourier, Laboratoire Mathématiques, n° 311, Grenoble 1995, 23 p.)

[Sa76] A. Sathaye - On linear planes. Proc. Amer. Math. Soc. 56 (1976) 1-7. | Article | MR 409472 | Zbl 0345.14013

[Sc89] G. W. Schwarz - Exotic algebraic group actions. C. R. Acad. Sci. Paris 309 (1989) 89-94. | MR 1004947 | Zbl 0688.14040

[Seg57] B. Segre - Corrispondenze di Möbius e transformazioni cremoniane intere. Atti Acad. Sci. Torino 91 (1957) 1-17. | MR 95175 | Zbl 0079.36801

[Se61] J.-P. Serre - Sur les modules projectifs. In Séminaire Dubreil-Pisot 1960/61, n°2. | Numdam | Zbl 0132.41301

[Se80] J.-P. Serre - Trees. Springer Verlag, Berlin-Heidelberg-New York, 1980. | MR 607504 | Zbl 0548.20018

[Sh66] I. R. Shafarevich - On some infinite dimensional groups. Rend. Mat. e Appl. (5) 25 (1966) 208-212. | MR 485898 | Zbl 0149.39003

[Sr91] V. Srinivas - On the embedding dimension of an affine variety. Math. Annalen 289 (1991) 125-132. | Article | MR 1087241 | Zbl 0725.14003

[Su89] T. Sugie - Algebraic characterization of the affine plane and the affine 3-space. In: Topological methods in algebraic transformation groups (H. Kraft et al., eds.). Progress in Math. vol. 80, Birkhäuser Verlag, Basel - Boston, 1989, pp. 177-190. | MR 1040864 | Zbl 0731.14027

[Suz74] M. Suzuki - Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l'espace ${ℂ}^2$. J. Math. Soc. Japan 26 (1974) 241-257. | Article | MR 338423 | Zbl 0276.14001

[tDP89] T. Tom Dieck, T. Petrie - Homology planes: An announcement and survey. In: Topological methods in algebraic transformation groups (H. Kraft et al., eds.). Progress in Math. vol. 80, Birkhäuser Verlag, Basel - Boston, 1989, pp. 27-48. | MR 1040856 | Zbl 0708.14024

[tDP90] T. Tom Dieck, T. Petrie - Contractible affine surfaces of Kodaira dimension one. Japan J. Math. 16 (1990) 147-169. | Article | MR 1064448 | Zbl 0721.14018

[Ku53] W. Van Der Kulk - On polynomial rings in two variables. Nieuw Arch. Wisk. 1 (1953) 33-41. | MR 54574 | Zbl 0050.26002

[Wi90] J. Winkelmann - On free holomorphic $ℂ$-actions on ${ℂ}^n$ and homogeneous Stein manifolds. Math. Ann. 286 (1990) 593-612. | Article | MR 1032948 | Zbl 0708.32004

[Wr79] D. Wright - Abelian subgroups of ${\mathrm{Aut}}_k\left(k[X,Y]\right)$ and applications to actions on the affine plane. Ill. J. Math. 23 (1979) 579-634. | MR 540400 | Zbl 0461.20011

[Za91] M. G. Zaidenberg - Ramanujam surfaces and exotic algebraic structures on ${ℂ}^n,n\ge 3$. Soviet Math. Dokl. 42 (1991) 636-640. | Zbl 0741.14016

[Za93] M. G. Zaidenberg - An analytic cancellation theorem and exotic algebraic structures on ${ℂ}^n,n\ge 3$. In: Astérisque 217 (1993), 251-282., 1993 (Max-Planck-Institut für Mathematik, Bonn, 1991. Preprint MPI/91-26, 33p.) | Zbl 0801.14001

[Za95] M. G. Zaidenberg - On exotic algebraic structures on affine spaces. In: Proceedings of a Conference "Geometric Complex Analysis". Tokyo, March 19-29, World Scientific, 1995 (Prépublication de l'Institut Fourier, Laboratoire de Mathématiques, n° 309, Grenoble 1995, 32 p.) | MR 1453650 | Zbl 0934.14042

[ZaL83] M. G. Zaidenberg, V. Ya. Lin - An irreducible simply connected algebraic curve in ${ℂ}^2$ is a quasihomogeneous curve. Soviet Math. Dokl. 28 (1983). | Zbl 0564.14014