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arxiv: 1512.01933 · v1 · pith:FQDAC4SYnew · submitted 2015-12-07 · 🧮 math.AG

Families of mathbb{A}¹-contractible affine threefolds

classification 🧮 math.AG
keywords contractiblethreefoldsaffinefamiliesmathbbansweringasokcase
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We provide families of affine threefolds which are contractible in the unstable $\mathbb A^1$-homotopy category of Morel-Voevodsky and pairwise non-isomorphic, thus answering a question of A. Asok and B. Doran. As a particular case, we show that the Koras-Russell threefolds of the first kind are contractible, extending results of M. Hoyois, A. Krishna and P. A. Ostvaer.

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