Braid monodromy of univariate fewnomials

Braid Monodromy of Special Curves

In this article, we compute the braid monodromy of two algebraic curves defined over R. These two curves are of complex level not bigger than 6, and they are unions of lines and conics. We use two different techniques for computing their braid monodromies. These results will be applied to computations of fundamental groups of their complements in C and CP.

Braid Monodromy and Topology of Plane Curves

In this paper we prove that braid monodromy of an affine plane curve determines the topology of a related projective plane curve. Introduction Our purpose in this paper is to relate the topological embedding of algebraic curves to a refinement of a well-known invariant of curves such as braid monodromy. Roughly speaking, braid monodromy is defined for a triple (C , L , P), where C ⊂ P2 is a cur...

On bifurcation braid monodromy of elliptic fibrations

Abstract. We define a monodromy homomorphism for irreducible families of regular elliptic fibrations which takes values in the mapping class group of a punctured sphere. In the computation we consider only elliptic fibrations which contain no singular fibres of types other than I1 and I ∗ 0 . We compare the maximal groups, which can be the monodromy groups of algebraic, resp. differentiable fam...

Braid Monodromy and Topology of Plane Curves

Braid Monodromy Factorization and Diffeomorphism Types

In this paper we prove that if two cuspidal plane curves B 1 and B 2 have equivalent braid monodromy factorizations, then B 1 and B 2 are smoothly isotopic in CP 2. As a consequence, we obtain that if the discriminant curves (or branch curves in other terminology) B 1 and B 2 of generic projections to CP 2 of surfaces of general type S 1 and S 2 , imbedded in a projective space by means of a mu...