Divides with cusps and Kirby diagrams for line arrangements

Abstract

The complement of a complexified real line arrangement is an affine surface. It is classically known that such a space has a handle decomposition up to $2$-handles. We will describe the handle decomposition induced from Lefschetz hyperplane section theorem for such a space. To describe the Kirby diagram, we introduce the notion of the divide with cusps which is a generalization of the divide introduced by A'Campo.