Families of $\mathbb{A}^1$-contractible affine threefolds

Abstract : We provide families of affine threefolds which are $\mathbb A^1$-contractible (that is, contractible in the unstable $\mathbb A^1$-homotopy category of Morel-Voevodsky) and pairwise non-isomorphic, thus answering a conjecture of Asok and Doran. As a particular case, we show that the Koras-Russell threefolds of the first kind are $\mathbb A^1$-contractible, extending results of Hoyois, Krishna and Ostvaer.
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https://hal.archives-ouvertes.fr/hal-01740827
Contributor : Imb - Université de Bourgogne <>
Submitted on : Thursday, March 22, 2018 - 2:05:43 PM
Last modification on : Thursday, September 5, 2019 - 11:44:03 AM

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Adrien Dubouloz, Jean Fasel. Families of $\mathbb{A}^1$-contractible affine threefolds. Algebraic Geometry, Foundation Compositio Mathematica, 2018, 5 (1), pp.1-14. ⟨10.14231/2018-001⟩. ⟨hal-01740827⟩

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