Kyoto Journal of Mathematics

Affine surfaces with isomorphic A2-cylinders

Adrien Dubouloz

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Abstract

We show that all complements of cuspidal hyperplane sections of smooth projective cubic surfaces have isomorphic A2-cylinders. As a consequence, we derive that the A2-cancellation problem fails in every dimension greater than or equal to 2.

Article information

Source
Kyoto J. Math., Volume 59, Number 1 (2019), 181-193.

Dates
Received: 5 December 2016
Revised: 30 January 2017
Accepted: 1 February 2017
First available in Project Euclid: 21 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1534838488

Digital Object Identifier
doi:10.1215/21562261-2018-0005

Mathematical Reviews number (MathSciNet)
MR3934627

Zentralblatt MATH identifier
07081626

Subjects
Primary: 14R05: Classification of affine varieties
Secondary: 14R25: Affine fibrations [See also 14D06] 14E07: Birational automorphisms, Cremona group and generalizations

Keywords
affine surfaces cylinders cancellation problem

Citation

Dubouloz, Adrien. Affine surfaces with isomorphic $\mathbb{A}^{2}$ -cylinders. Kyoto J. Math. 59 (2019), no. 1, 181--193. doi:10.1215/21562261-2018-0005. https://projecteuclid.org/euclid.kjm/1534838488


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