We introduce Koras-Russell fiber bundles over algebraically closed fields of characteristic zero. After a single suspension, this exhibits an infinite family of smooth affine 1-contractible 3-folds. Moreover, we give examples of stably 1-contractible smooth affine 4-folds containing a Brieskorn-Pham surface, and a family of smooth affine 3-folds with a higher-dimensional 1-contractible total space.
A(1)-contractibility of Koras-Russell threefolds / M. Hoyois, A. Krishna, P.A. Oestvaer. - In: ALGEBRAIC GEOMETRY. - ISSN 2214-2584. - 3:4(2016), pp. 407-423. [10.14231/AG-2016-019]
A(1)-contractibility of Koras-Russell threefolds
P.A. Oestvaer
2016
Abstract
We introduce Koras-Russell fiber bundles over algebraically closed fields of characteristic zero. After a single suspension, this exhibits an infinite family of smooth affine 1-contractible 3-folds. Moreover, we give examples of stably 1-contractible smooth affine 4-folds containing a Brieskorn-Pham surface, and a family of smooth affine 3-folds with a higher-dimensional 1-contractible total space.
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