Searcharxiv⌕ Search

arXiv subjects

Meirav Amram

Publications and source records attributed to Meirav Amram.

30 records · Page 2Linked to original sources
arXiv2012

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.

math.AG↗
arXiv2010

Classification of Fundamental Groups of Galois Covers of Surfaces of Small Degree Degenerating to Nice Plane Arrangements

Let $X$ be a surface of degree $n$, projected onto $\mathbb{CP}^2$. The surface has a natural Galois cover with Galois group $S_n.$ It is possible to determine the fundamental group of a Galois cover from that of the complement of the branch curve of $X.$ In this paper we survey the fundamental groups of Galois covers of all surfaces of small degree $n \leq 4$, that degenerate to a nice plane arrangement, namely a union of $n$ planes such that no three planes meet in a line. We include the already classical examples of the quadric, the Hirzebruch and the Veronese surfaces and the degree $4$ embedding of $\mathbb{CP}^1 \times \mathbb{CP}^1,$ and also add new computations for the remaining cases: the cubic embedding of the Hirzebruch surface $F_1$, the Cayley cubic (or a smooth surface in the same family), for a quartic surface that degenerates to the union of a triple point and a plane not through the triple point, and for a quartic $4$-point. In an appendix, we also include the degree $8$ surface $\mathbb{CP}^1\times \mathbb{CP}^1$ embedded by the $(2,2)$ embedding, and the degree $2n$ surface embedded by the $(1,n)$ embedding, in order to complete the classification of all embeddings of $\mathbb{CP}^1 \times \mathbb{CP}^1,$ which was begun in \cite{15}.

math.AG↗
arXiv2008

The fundamental group of Galois cover of the surface ${\mathbb T} \times {\mathbb T}$

This is the final paper in a series of four, concerning the surface $T \times T$ embedded in $\mathbb{CP}^8$, where $T$ is a the one dimensional torus. In this paper we compute the fundamental group of the Galois cover of the surface with respect to a generic projection onto $\mathbb{CP}^2$, and show that it is nilpotent of class 3. This is the first time such a group is presented as the fundamental group of a Galois cover of a surface.

math.AG↗
arXiv2006

Fundamental groups of Tangent Conic-Line arrangements with Singularities up to order 6

We list all the possible fundamental groups of the complements of real conic-line arrangements with two conics which are tangent to each other at two points, with up to two additional lines. For the computations we use the topological local braid monodromies and the techniques of Moishezon-Teicher and van-Kampen. We also include some conjectures concerning the connection between the presentation of the fundamental group of the complements and the geometry of an interesting family of conic line arrangements.

math.GT↗
arXiv2004

Higher degree Galois covers of CP^1 x T

Let T be a complex torus, and X the surface CP^1 x T. If T is embedded in CP^{n-1} then X may be embedded in CP^{2n-1}. Let X_Gal be its Galois cover with respect to a generic projection to CP^2. In this paper we compute the fundamental group of X_Gal, using the degeneration and regeneration techniques, the Moishezon-Teicher braid monodromy algorithm and group calculations. We show that pi_1(X_Gal) = Z^{4n-2}.

math.AG↗
arXiv2002

Fundamental groups of some quadric-line arrangements

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 not in Q. The last arrangement consists of a quadric Q with n lines passing through a point p in Q.

math.AG↗
arXiv2002

Braid Monodromy of Special Curve

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^2 and C PP^2.

math.AG↗
arXiv2002

The fundamental group of a Galois cover of CP^1 X T

Let T be the complex projective torus, and X the surface CP^1 X T. Let X_Gal be its Galois cover with respect to a generic projection to CP^2. In this paper we compute the fundamental group of X_Gal, using the degeneration and regeneration techniques, the Moishezon-Teicher braid monodromy algorithm and group calculations. We show that pi_1(X_Gal) = Z^10.

math.AG↗