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

Qile Chen; Yi Zhu

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

Algebraic Geometry 2017-02-21 v4

Authors: Qile Chen , Yi Zhu

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.

Keywords

algebraic curves curves toric varieties

Cite

@article{arxiv.1407.5476,
  title  = {$\mathbb{A}^1$-curves on log smooth varieties},
  author = {Qile Chen and Yi Zhu},
  journal= {arXiv preprint arXiv:1407.5476},
  year   = {2017}
}

Comments

37 pages, Improved exposition, More examples of $\mathbb{A}^1$-connected varieties given by complements of ample divisors are included, see Theorem 1.5

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

Abstract

Keywords

Cite

Comments

Related papers