$\mathbb{A}^1$ curves on log K3 surfaces

TL;DR

This paper classifies certain log K3 surfaces that admit infinitely many algebraic curves of type $ ext{A}^1$, advancing understanding of their geometric properties.

Contribution

It provides a complete classification of type II log K3 surfaces with countably infinite $ ext{A}^1$ curves, a new result in algebraic geometry.

Findings

Classification of all type II log K3 surfaces with infinitely many $ ext{A}^1$ curves

Identification of conditions for the existence of countably infinite $ ext{A}^1$ curves

Advancement in understanding the geometry of log K3 surfaces

Abstract

In this paper, we study $\mathbb{A}^1$ curves on log K3 surfaces. We classify all genuine log K3 surfaces of type II which admits countably infinite $\mathbb{A}^1$ curves.