Links arising from braid monodromy factorizations

TL;DR

This paper explores how braid monodromy factorizations relate to the links formed by their closures, especially in the context of algebraic surfaces and line-conic arrangements, revealing link invariance under different local configurations.

Contribution

It provides a detailed analysis of the local contributions of braid monodromy in algebraic surfaces and arrangements, highlighting conditions for link invariance despite different local configurations.

Findings

Links can be equivalent even with different local arrangements.

Degenerations involving intersection points of multiplicity two and three are key.

Braid monodromy captures essential topological information of the links.

Abstract

We investigate the local contribution of the braid monodromy factorization in the context of the links obtained by the closure of these braids. We consider plane curves which are arrangements of lines and conics as well as some algebraic surfaces, where some of the former occur as local configurations in degenerated and regenerated surfaces in the latter. In particular we focus on degenerations which involve intersection points of multiplicity two and three. We demonstrate when the same links arise even when the local arrangements are different.