affine open subsets in \mathbb{A}^{3} without the cancellation property

Authors :: Dubouloz, Adrien
Institut de Mathématiques de Bourgogne [Dijon] (IMB)
Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC)
Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB)
Institut de Mathématiques de Bourgogne [Dijon] ( IMB )
Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS )
Publication Year :: 2011
Publisher :: HAL CCSD, 2011.
Abstract: We give families of examples of principal open subsets of the affine space \mathbb{A}^{3} which do not have the cancellation property. We show as a by-product that the cylinders over Koras-Russell threefolds of the first kind have a trivial Makar-Limanov invariant.

Subjects :: Mathematics::Algebraic Geometry
Mathematics::Commutative Algebra
Cancellation problem
Mathematics::Rings and Algebras
14R10
14R20
Koras-Russell threefolds
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]

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