@incollection{SB_1994-1995__37__295_0, author = {Kraft, Hanspeter}, title = {Challenging problems on affine <span class="mathjax-formula">$n$</span>-space}, booktitle = {S\'eminaire Bourbaki : volume 1994/95, expos\'es 790-804}, author = {Collectif}, series = {Ast\'erisque}, note = {talk:802}, publisher = {Soci\'et\'e math\'ematique de France}, number = {237}, year = {1996}, zbl = {0892.14003}, mrnumber = {1423629}, language = {en}, url = {archive.numdam.org/item/SB_1994-1995__37__295_0/} }
Kraft, Hanspeter. Challenging problems on affine $n$-space, dans Séminaire Bourbaki : volume 1994/95, exposés 790-804, Astérisque, no. 237 (1996), Exposé no. 802, 23 p. http://archive.numdam.org/item/SB_1994-1995__37__295_0/
[AC95] Geometry of plane curves via Tschirnhausen resolution towers. J. Alg. Geometry (1995) (to appear). | Zbl 0904.14014
, -[AbM75] Embeddings of the line in the plane. J. Reine Angew. Math. 276 (1975) 149-166. | EuDML 151610 | MR 379502 | Zbl 0332.14004
, -[As94] Non-linearizable algebraic group actions on . J. Algebra 166 (1994) 72-79. | Article | Zbl 0817.14027
-[Ba84] A non-triangular action of on . J. Pure Appl. Algebra 33 (1984) 1-5. | Article | MR 750225 | Zbl 0555.14019
-[BaH85] Linearizing certain reductive group actions. Trans. Amer. Math. Soc. 292 (1985) 463-482. | Article | MR 808732 | Zbl 0602.14047
, -[BaH87] Some equivariant -theory of affine algebraic group actions. Comm. Algebra 15 (1987) 181-217. | Article | MR 876977 | Zbl 0612.14047
, -[Bi66] Remarks on the action of an algebraic torus on , I. Bull. Acad. Polon. Sci. Sér. Sci. Math. 14 (1966) 177-181. | Zbl 0163.42901
-[Bi67] Remarks on the action of an algebraic torus on , II. Bull. Acad. Polon. Sci. Sér. Sci. Math. 15 (1967) 123-125. | Zbl 0163.42901
-[Bi76] 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] 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] On the cancellation problem and automorphism group of affine algebraic varieties. Preprint 1989. (Appendix by K. Fieseler)
-[Di90] Hypersurfaces in diffeomorphic to . Max-Planck Institut Bonn, preprint 1990.
-[Di92] Singularities and topology of hypersurfaces. Universitext, Springer Verlag, Berlin-Heidelberg-New York, 1992. | Article | MR 1194180 | Zbl 0753.57001
-[DMP89] Fixed point free algebraic actions on varieties diffeomorphic to . 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] 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] Fixed points for reductive group actions on acyclic varieties. Ann. Inst. Fourier (1995) to appear. (Thesis Basel 1994) | EuDML 75159 | Numdam | MR 1370747
-[Fi94] On complex affine surfaces with -action. Comment. Math. Helv. 69 (1994) 5-27. | Article | EuDML 140323 | MR 1259603 | Zbl 0806.14033
-[Fu79] On Zariski problem. Proc. Japan Acad. Ser. A. Math. Sci. 55 (1979) 106-110. | Article | MR 531454 | Zbl 0444.14026
-[Fu81] Cancellation problem for complete varieties. Invent. Math. 64 (1981) 119-121. | Article | EuDML 142816 | MR 621772 | Zbl 0462.14001
-[Fu82] On the topology of non-complete surfaces. J. Fac. Sci. Univ. Tokyo 29 (1982) 503-566. | MR 687591 | Zbl 0513.14018
-[GiD75] Automorphisms of affine surfaces, I. Math. USSR-Izv. 9 (1975) 493-534. | Article | MR 376701 | Zbl 0331.14007
, -[Gu88] 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] Affine surfaces with . In: "Algebraic Geometry and Commutative Algebra" in Honor of Masayoshi Nagata., 1987, pp. 99-124. | Zbl 0707.14015
, -[GuM95] On contractible curves in . Preprint 1995.
, -[HeK94] An equivariant version of Grauert's Oka principle. Invent. Math. 119 (1994) 317-346. | Article | EuDML 144259 | MR 1312503 | Zbl 0837.32004
, -[Ho72] Nonuniqueness of coefficient rings in a polynomial ring. Proc. Amer. Math. Soc. 34 (1972) 81-82. | Article | MR 294325 | Zbl 0233.13012
-[HsS86] Actions of compact connected Lie groups on acyclic manifolds with low dimensional orbit space. J. Reine Angew. Math. 369 (1986) 21-39. | EuDML 152849 | MR 850627 | Zbl 0583.57025
, -[Ii82] 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] Cancellation theorem for algebraic varieties. J. Fac. Sci. Univ. Tokyo 24 (1977) 123-127. | MR 450278 | Zbl 0353.14013
, -[Je87] The extension of regular and rational embeddings. Math. Ann. 113 (1987) 113-120. | Article | EuDML 164238 | MR 884649 | Zbl 0611.14010
-[Je91] Identity sets for polynomial automorphisms. J. Pure Appl. Algebra 76 (1991) 333-339. | Article | MR 1147306 | Zbl 0752.14010
-[Je92] The Jacobian Conjecture and the extension of a polynomial embeddings. Math. Annalen 294 (1992) 289-293. | Article | EuDML 165003 | MR 1183407 | Zbl 0757.14007
-[Je93] Irreducible identity sets for polynomial automorphisms. Math. Zeitschrift 212 (1993) 601-617. | Article | EuDML 174508 | MR 1214049 | Zbl 0806.14011
-[Je94] Affine smooth varieties with finite group of automorphisms. Math. Zeitschrift 216 (1994) 575-591. | Article | EuDML 174669 | MR 1288046 | Zbl 0824.14012
-[Ju42] Über ganze birationale Transformationen der Ebene. J. Reine Angew. Math. 184 (1942) 161-174. | EuDML 150111 | JFM 68.0382.01 | MR 8915
-[Ka91] Extensions of isomorphisms between affine algebraic subvarieties of to automorphisms of . Proc. Amer. Math. Soc. 113 (1991) 325-334. | MR 1076575 | Zbl 0743.14011
-[Ka93] Smooth contractible hypersurfaces in and exotic algebraic structures on . Math. Zeitschrift 214 (1993) 499-510. | Article | EuDML 174584 | MR 1245209 | Zbl 0792.57013
-[Ka95] Exotic structures on and -actions on . 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] Affine algebraic manifolds without dominant morphisms from euclidean space. Preprint 1995. | MR 1466159 | Zbl 0951.14007
, -[KaM95b] On Russell's contractible threefolds. Preprint 1995.
, -[Kam75] On the absence of nontrivial separable forms of the affine plane. J. Algebra 35 (1975) 449-456. | Article | MR 369380 | Zbl 0309.14029
-[Kam79] 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] 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] On linearizing algebraic torus actions. J. Pure Appl. Algebra 23 (1982) 243-250. | Article | MR 644276 | Zbl 0518.14026
, -[Kn91] Nichtlinearisierbare Operationen halbeinfacher Gruppen auf affinen Räumen. Invent. Math. 105 (1991) 217-220. | Article | EuDML 143911 | MR 1109627 | Zbl 0739.20019
-[KoR86] -actions on . In: Canad. Math. Soc. Confer. Proc.. vol. 6, 1986, pp. 269-276. | MR 846023 | Zbl 0591.14034
, -[KoR89a] Codimension torus actions on affine -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] On linearizing "good" -actions on . 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] Contractible algebraic threefolds and -actions on . Preprint 1995. | Zbl 0882.14013
, -[Kr89a] 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] -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] -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] Semisimple group actions on the three dimensional affine space are linear. Comment. Math. Helv. 60 (1985) 466-479. | Article | EuDML 140027 | MR 814152 | Zbl 0645.14020
, -[KrS89] 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] Reductive group actions with one-dimensional quotient. Publ. Math. IHES 76 (1992) 1-97. | Article | EuDML 104084 | Numdam | MR 1215592 | Zbl 0783.14026
, -[KrS95] Finite automorphisms of affine -space. In: Proceedings of the Curaçao Conference on "Automorphisms of Affine Space". to appear, 1995 | Article | MR 1352703 | Zbl 0837.14010
, -[Li77] 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] Slices étales. Bull. Soc. Math. France, Mémoire 33 (1973) 81-105. | Article | EuDML 94648 | Numdam | MR 342523 | Zbl 0286.14014
-[Ma94] On the hypersurface in . Preprint 1994. | MR 1289046
-[MMP91] 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] The equivariant Serre Problem for abelian groups. J. Amer. Math. Soc (1995). | MR 1380501 | Zbl 0884.14007
, , -[MaP91] 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] Moduli of equivariant -vector bundles. Thesis Brandeis 1995.
-[Mi87] Algebraic characterization of the affine 3-space. Proc. Alg. Geometry Seminar, Singapore, World Scientific, 1987, pp. 53-67. | MR 966444
-[MiS80] Affine surfaces containing cylinderlike open sets. J. Math. Kyoto Univ. 20 (1980) 11-42. | Article | MR 564667 | Zbl 0445.14017
, -[MiT87] Open algebraic surfaces with Kodaira dimension -. Proc. Sympos. Pure Math. 46 (1987) 435-450. | Article | Zbl 0643.14021
, -[Na67] A theorem on valuation rings and its applications. Nagoya Math. J. 29 (1967) 85-91. | Article | MR 207688 | Zbl 0146.26302
-[Ne89a] 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] Complex algebraic plane curves via their links at infinity. Invent. math. 98 (1989) 445-489. | Article | EuDML 143738 | MR 1022302 | Zbl 0734.57011
-[Pa84] Semisimple automorphism groups of four-dimensional affine space. Math. USSR-Izv. 23 (1984) 171-183. | Article | Zbl 0581.14033
-[PeR86] Finite-order algebraic automorphisms of affine varieties. Comment. Math. Helv. 61 (1986) 203-221. | Article | EuDML 140049 | MR 856087 | Zbl 0612.14046
, -[Ra71] 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] Opérations du groupe additif sur le plan affine. C. R. Acad. Sci. Paris 267 A (1968) 384-387. | MR 232770 | Zbl 0165.05402
-[Rud82] Embedding of the line in the plane. J. Reine Angew. Math. 337 (1982) 113-118. | EuDML 152483 | MR 676044 | Zbl 0486.14003
-[Ru81] On affine-ruled rational surfaces. Math. Ann. 255 (1981) 287-302. | Article | EuDML 182840 | MR 615851 | Zbl 0438.14024
-[Ru92] On a class of -like threefolds. Preliminary report 1992.
-[Ru95] Open problems on open algebraic varieties (Montreal 1994 Problems). Prépublication de l'Institut Fourier, Laboratoire Mathématiques, n° 311, Grenoble 1995, 23 p.)
-[Sa76] On linear planes. Proc. Amer. Math. Soc. 56 (1976) 1-7. | Article | MR 409472 | Zbl 0345.14013
-[Sc89] Exotic algebraic group actions. C. R. Acad. Sci. Paris 309 (1989) 89-94. | MR 1004947 | Zbl 0688.14040
-[Seg57] Corrispondenze di Möbius e transformazioni cremoniane intere. Atti Acad. Sci. Torino 91 (1957) 1-17. | MR 95175 | Zbl 0079.36801
-[Se61] Sur les modules projectifs. In Séminaire Dubreil-Pisot 1960/61, n°2. | EuDML 111203 | Numdam | Zbl 0132.41301
-[Se80] Trees. Springer Verlag, Berlin-Heidelberg-New York, 1980. | MR 607504 | Zbl 0548.20018
-[Sh66] On some infinite dimensional groups. Rend. Mat. e Appl. (5) 25 (1966) 208-212. | MR 485898 | Zbl 0149.39003
-[Sr91] On the embedding dimension of an affine variety. Math. Annalen 289 (1991) 125-132. | Article | EuDML 164772 | MR 1087241 | Zbl 0725.14003
-[Su89] 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] Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l'espace . J. Math. Soc. Japan 26 (1974) 241-257. | Article | MR 338423 | Zbl 0276.14001
-[tDP89] 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] Contractible affine surfaces of Kodaira dimension one. Japan J. Math. 16 (1990) 147-169. | Article | MR 1064448 | Zbl 0721.14018
, -[Ku53] On polynomial rings in two variables. Nieuw Arch. Wisk. 1 (1953) 33-41. | MR 54574 | Zbl 0050.26002
-[Wi90] On free holomorphic -actions on and homogeneous Stein manifolds. Math. Ann. 286 (1990) 593-612. | Article | EuDML 164652 | MR 1032948 | Zbl 0708.32004
-[Wr79] Abelian subgroups of and applications to actions on the affine plane. Ill. J. Math. 23 (1979) 579-634. | MR 540400 | Zbl 0461.20011
-[Za91] Ramanujam surfaces and exotic algebraic structures on . Soviet Math. Dokl. 42 (1991) 636-640. | Zbl 0741.14016
-[Za93] An analytic cancellation theorem and exotic algebraic structures on . In: Astérisque 217 (1993), 251-282., 1993 (Max-Planck-Institut für Mathematik, Bonn, 1991. Preprint MPI/91-26, 33p.) | Zbl 0801.14001
-[Za95] 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] An irreducible simply connected algebraic curve in is a quasihomogeneous curve. Soviet Math. Dokl. 28 (1983). | Zbl 0564.14014
, -