Neighborhood of a rational curve with an ordinary cusp

TL;DR

This paper studies the complex analytic properties of neighborhoods around a rational curve with an ordinary cusp in a smooth surface, focusing on cases where the curve's self-intersection number is zero.

Contribution

It provides new insights into the local complex structure of neighborhoods of rational cuspidal curves with zero self-intersection in complex surfaces.

Findings

Characterization of neighborhoods around rational cuspidal curves

Conditions for the existence of certain complex structures

Implications for the classification of complex surfaces

Abstract

We investigate complex analytic properties of a neighborhood of a reduced rational curve with an ordinary cusp embedded in a non-singular complex surface whose self-intersection number is zero.