On a new class of rational cuspidal plane curves with two cusps

TL;DR

This paper classifies a special class of rational cuspidal plane curves with two cusps, focusing on their geometric properties and the behavior of their strict transforms after resolution.

Contribution

It introduces a classification of rational cuspidal plane curves with two cusps based on the maximal self-intersection property of their strict transforms.

Findings

Classification of such curves with specific geometric properties

Identification of conditions for maximal self-intersection

Insights into the structure of curves with logarithmic Kodaira dimension two

Abstract

In this paper, we consider rational cuspidal plane curves having exactly two cusps whose complements have logarithmic Kodaira dimension two. We classify such curves with the property that the strict transforms of them via the minimal embedded resolution of the cusps have maximal self-intersection number.