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Challenging problems in affine n-space

Kraft, Hanspeter. (1996) Challenging problems in affine n-space. Astérisque, 47 (802). pp. 295-317.

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Abstract

Complex affine n-space C^n, the basic object of algebraic geometry, offers a number of exciting and striking problems. The most famous one, the Jacobian Conjecture is the still unsolved. Others are the Cancellation Problem (Does Y times C^k simeq C^{n+k} imply that Y simeq C^n?), the Linearization Problem (Is every automorphism of C^n of finite order conjugate to a linear automorphism?), or the Embedding Problem (Are there other embeddings of C^{n-1} into C^n than the standard ones?). It turns out that these questions and several others are intimately related and have very interesting connections with problems arising from algebraic group actions and orbit spaces. We give a survey on these problems and discuss some recent progress and examples.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft)
UniBasel Contributors:Kraft, Hanspeter
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Note:Also published in: Séminaire Bourbaki 1994/95. - Paris : Société mathématique de France. - Exposée 802, S. 295-317 -- Publication type according to Uni Basel Research Database: Journal article
Language:English
Last Modified:21 Sep 2017 06:46
Deposited On:08 Jun 2012 06:47

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