Some knot theory of complex plane curves

TL;DR

This survey reviews topological aspects of how complex curves are embedded in complex surfaces, highlighting key problems and developments in the field since its original publication in 1983.

Contribution

It provides a comprehensive overview of the topological placement problem for complex curves in surfaces, including updates and corrections to the original 1983 survey.

Findings

Summarizes key topological techniques for complex curve placement

Highlights unresolved questions and recent progress in the field

Provides corrected and updated references for further research

Abstract

This survey of some of the more topological aspects of the placement problem for complex curves in complex surfaces was originally published in L'Enseignement Mathematique 29 (1983). The present LaTeXed redaction corrects several typographical errors without, I hope, introducing new ones; some minor emendations and references to post-1983 results have been added as footnotes, but I have not made a thoroughgoing effort to update the text. Anyone having further information -- for instance, on the current status of questions incorrectly described as still open -- is encouraged to let me know!