Handle decompositions and Kirby diagrams for the complement of plane algebraic curves

Abstract

The complement of plane algebraic curves are well studied from topological and algebro-geometric viewpoints. In this paper, we will describe the explicit handle decompositions and the Kirby diagrams for the complement of plane algebraic curves. The method is based on the notion of braid monodromy. We refined this technique to obtain handle decompositions and Kirby diagrams.