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

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.

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

References in corpus (5)

• Spherical homogeneous spaces of minimal rank
• The Evaluation Space of Logarithmic Stable Maps
• Remarks about bubbles
• Positivity criteria for log canonical divisors and hyperbolicity
• Strong approximation over function fields

Cited by in corpus (2)

• Strong approximation over function fields
• Log rationally connected surfaces