Meirav Amram

On the Degeneration, Regeneration and Braid Monodromy of T×T

This paper is the first in a series of three papers concerning the surface T×T. Here we study the degeneration of T×T and the regeneration of its degenerated object. We also study the braid monodromy and its regeneration.

Fundamental groups of some quadric-line arrangements

Abstract In this paper we obtain presentations of fundamental groups of the complements of three quadric-line arrangements in P 2 . The first arrangement is a smooth quadric Q with n tangent lines to Q , and the second one is a quadric Q with n lines passing through a point p ∉ Q . The last arrangement consists of a quadric Q with n lines passing through a point p ∈ Q .

THE FUNDAMENTAL GROUP OF GALOIS COVER OF THE SURFACE 𝕋 × 𝕋

This is the final paper in a series of four, concerning the surface 𝕋 × 𝕋 embedded in ℂℙ8, where 𝕋 is the one-dimensional torus. In this paper we compute the fundamental group of the Galois cover o...

THE FUNDAMENTAL GROUP OF THE GALOIS COVER OF HIRZEBRUCH SURFACE F1(2, 2)

This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces Fk(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is where c = gcd(a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface F1(2, 2), compute the braid monodromy factorization of the branch curve in ℂ2, and verify that, in this case, the conjecture holds: the fundamental group of the Galois cover of F1(2, 2) with respect to a generic projection is isomorphic to .

On the fundamental group of the complement of two real tangent conics and an arbitrary number of real tangent lines

We compute the simplified presentations of the fundamental groups of the complements of the family of real conic-line arrangements with up to two conics which are tangent to each other at two points, with an arbitrary number of tangent lines to both conics. All the resulting groups turn out to be big.

COXETER COVERS OF THE CLASSICAL COXETER GROUPS

Let C(T) be a generalized Coxeter group, which has a natural map onto one of the classical Coxeter groups, either Bn or Dn. Let CY(T) be a natural quotient of C(T), and if C(T) is simply-laced (which means all the relations between the generators has order 2 or 3), CY(T) is a generalized Coxeter group, too. Let At,n be a group which contains t Abelian groups generated by n elements. The main result in this paper is that CY(T) is isomorphic to At,n ⋊ Bn or At,n ⋊ Dn, depends on whether the signed graph T contains loops or not, or in other words C(T) is simply-laced or not, and t is the number of the cycles in T. This result extends the results of Rowen, Teicher and Vishne to generalized Coxeter groups which have a natural map onto one of the classical Coxeter groups.

Links arising from braid monodromy factorizations

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.