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Article Dans Une Revue International Journal of Mathematics Année : 2019

$\mathbb{A}^1$-contractibility of affine modifications


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 A1-contractible 3-folds. Moreover, we give examples of stably A1-contractible smooth affine 4-folds containing a Brieskorn–Pham surface, and a family of smooth affine 3-folds with a higher-dimensional A1-contractible total space.

Dates et versions

hal-02421194 , version 1 (20-12-2019)



Adrien Dubouloz, Sabrina Pauli, Paul Arne Østvær. $\mathbb{A}^1$-contractibility of affine modifications. International Journal of Mathematics, 2019, pp.1950069. ⟨10.1142/S0129167X19500691⟩. ⟨hal-02421194⟩
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