Symplectic isotopy of rational cuspidal sextics and septics

TL;DR

This paper classifies rational cuspidal curves of degrees 6 and 7 in the complex projective plane up to symplectic isotopy, employing topological, pseudoholomorphic, and birational methods.

Contribution

It provides a comprehensive classification of these curves up to symplectic isotopy, combining multiple advanced techniques.

Findings

Complete classification of degree 6 and 7 rational cuspidal curves

Identification of symplectic isotopy classes

Application of pseudoholomorphic techniques in classification

Abstract

We classify rational cuspidal curves of degrees 6 and 7 in the complex projective plane, up to symplectic isotopy. The proof uses topological tools, pseudoholomorphic techniques, and birational transformations.