$\mathbb{A}^1$-curves on affine complete intersections

TL;DR

This paper extends previous results on rational curves and zero cycles from projective complete intersections to the logarithmic setting, broadening the understanding of algebraic cycles in more general geometric contexts.

Contribution

It introduces a logarithmic framework for studying rational curves and zero cycles on affine complete intersections, generalizing classical results.

Findings

Established existence of rational curves in the logarithmic setting.

Extended classical results to affine complete intersections.

Provided new tools for studying algebraic cycles in logarithmic geometry.

Abstract

We generalize the results of Clemens, Ein, and Voisin regarding rational curves and zero cycles on generic projective complete intersections to the logarithmic setup.