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arXiv · 1407.5476

$\mathbb{A}^1$-curves on log smooth varieties

Qile Chen·Yi Zhu
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Abstract

In this paper, we study $\mathbb{A}^1$-connected varieties from log geometry point of view, and prove a criterion for $\mathbb{A}^1$-connectedness. As applications, we provide many interesting examples of $\mathbb{A}^1$-connected varieties in the case of complements of ample divisors, and the case of homogeneous spaces. We also obtain a logarithmic version of Hartshorne's conjecture characterizing projective spaces and affine spaces.

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Qile Chen, Yi Zhu. 2017-02-18. $\mathbb{A}^1$-curves on log smooth varieties. https://arxiv.org/abs/1407.5476

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