Affine surfaces containing cylinderlike open sets

Miyanishi, Masayoshi; Sugie, Tohru

doi:10.1215/kjm/1250522319

Cited by 135 publications

(79 citation statements)

References 3 publications

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“…Now let's return to the cancellation problems described above. (For more details we refer to the paper [36] by Kraft, the papers [33] and [34] by Kang, the paper [57] by Sugie and the paper [45] by Miyanishi and Sugie. )…”

Section: Cancellation Problemsmentioning

confidence: 99%

Polynomial automorphisms and the Jacobian conjecture, by Arno van den Essen. Progress in Mathematics 190. Pp. 352. SFr 98. 2000. ISBN 3 7643 6350 9 (Birkhäuser).

Abbott¹

2001

Math. Gaz.

142

258

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In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalent descriptions are given and various related conjectures are discussed. At the end of the paper, we discuss the recent counter-examples, in all dimensions greater than two, to the Markus-Yamabe conjecture (Global asymptotic Jacobian conjecture). RésuméDans ce papier nous présentons un rapport actualisé sur les résultats les plus importants concernant la conjecture Jacobienne : plusieurs formulations équivalentes et diverses conjectures connexes sont considérées. A la fin du papier, nous donnons les contre-exemples récents, en toute dimension plus grande que deux, à la conjecture de Markus-Yamabe.

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Section: Cancellation Problemsmentioning

confidence: 99%

Polynomial automorphisms and the Jacobian conjecture, by Arno van den Essen. Progress in Mathematics 190. Pp. 352. SFr 98. 2000. ISBN 3 7643 6350 9 (Birkhäuser).

Abbott¹

2001

Math. Gaz.

142

258

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“…This problem remains unsolved in general, but has a positive answer if dim Y ≤ 2 [9]. Obviously, Y is a smooth contractible affine variety.…”

Section: Cancellation Problemmentioning

confidence: 99%

The Role Of Exotic Affine Spaces In the Classification Of Homogeneous Affine Varieties

Snow

2004

Encyclopaedia of Mathematical Sciences

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“…Let us recall that an affine variety X has the cancellation property (CP) if for every affine variety Y , if X ×k ∼ = Y × k, then X ∼ = Y (see e.g. [1], [3], [4], [5], [6], [11]). Let X be an affine variety over k with dim X ≥ 7.…”

Section: Introductionmentioning

confidence: 99%