On complex affine surfaces with ℂ+-action

Fieseler, Karl-Heinz

doi:10.1007/bf02564471

Cited by 77 publications

(62 citation statements)

References 4 publications

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“…Then there are well-known counterexamples due to Daniel-ewski [4], Fieseler [6], tom Dieck [5], and Wilkens [22]. In tom Dieck [5], it is shown that the smooth affine surfaces V (d, In the present article, we observe various properties of affine pseudo-planes and their universal coverings.…”

Section: Equivariant Cancellation Problem Let X and Y Be Smooth Affimentioning

confidence: 49%

Affine pseudo-planes and cancellation problem

Masuda

Miyanishi

2005

Trans. Amer. Math. Soc.

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Abstract. We define affine pseudo-planes as one class of Q-homology planes. It is shown that there exists an infinite-dimensional family of non-isomorphic affine pseudo-planes which become isomorphic to each other by taking products with the affine line A 1 . Moreover, we show that there exists an infinitedimensional family of the universal coverings of affine pseudo-planes with a cyclic group acting as the Galois group, which have the equivariant non-cancellation property. Our family contains the surfaces without the cancellation property, due to Danielewski-Fieseler and tom Dieck.

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Section: Equivariant Cancellation Problem Let X and Y Be Smooth Affimentioning

confidence: 49%

Affine pseudo-planes and cancellation problem

Masuda

Miyanishi

2005

Trans. Amer. Math. Soc.

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“…In [4] and in [2] , the abstract notion of Danielewski surfaces was developed, and these surfaces were classified.…”

Section: Cedrammentioning

confidence: 99%

Embeddings of a family of Danielewski hypersurfaces and certain \mathbf{C}^+-actions on \mathbf{C}^3

Moser-Jauslin¹,

Poloni²

2006

Ann. inst. Fourier

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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%