Additive group actions on Danielewski varieties and the Cancellation Problem

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dc.creatorDubouloz, Adrien
dc.date2005-07-25
dc.date.accessioned2026-07-07T05:21:58Z
dc.date.available2026-07-07T05:21:58Z
dc.descriptionThe cancellation problem asks if two complex algebraic varieties X and Y of the same dimension such that X\times\mathbb{C} and Y\times\mathbb{C} are isomorphic are isomorphic. Iitaka and Fujita established that the answer is positive for a large class of varieties of any dimension. In 1989, Danielewski constructed a famous counter-example using smooth affine surfaces with additive group actions. His construction was further generalized by Fieseler and Wilkens to describe a larger class of affine surfaces. Here we construct higher dimensional analogues of these surfaces. We study algebraic actions of the additive group \mathbb{C}\_{+} on certain of these varieties, and we obtain counter-examples to the cancellation problem in any dimension n\geq2 .
dc.description12p
dc.identifierhttps://arxiv.org/abs/math/0507505
dc.identifierhttp://arxiv.org/abs/math/0507505
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75889
dc.subjectAlgebraic Geometry
dc.subject14R10; 14R20
dc.titleAdditive group actions on Danielewski varieties and the Cancellation Problem
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