arXiv subjects

M. Amram

Publications and source records attributed to M. Amram.

6 recordsLinked to original sources

arXiv2008

Fundamental group for the complement of the Cayley's singularities

Given a singular surface X, one can extract information on it by investigating the fundamental group $π_1(X - Sing_X)$. However, calculation of this group is non-trivial, but it can be simplified if a certain invariant of the branch curve of X - called the braid monodromy factorization - is known. This paper shows, taking the Cayley cubic as an example, how this fundamental group can be computed by using braid monodromy techniques and their liftings. This is one of the first examples that uses these techniques to calculate this sort of fundamental group.

math.AG↗

arXiv2008

Braid monodromy factorization for a non-prime $K3$ surface branch curve

This paper is the second in a series. The first one describes pillow degenerations of a $K3$ surface with genus $g$. In this paper we study the $(2,2)$-pillow degeneration of a non-prime $K3$ surface and the braid monodromy of the branch curve of the surface with respect to a generic projection onto $\C¶^2$. In future papers we study the fundamental group of the complement of the branch curve and the fundamental group of the Galois cover of the surface with respect to this generic projection.

math.AG↗

arXiv2008

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 $B_n$ or $D_n$. Let $C_Y(T)$ 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), $C_Y(T)$ is a generalized Coxeter group, too . Let $A_{t,n}$ be a group which contains $t$ Abelian groups generated by $n$ elements. The main result in this paper is that $C_Y(T)$ is isomorphic to $A_{t,n} \semidirect B_n$ or $A_{t,n} \semidirect D_n$, 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.

math.GR↗

arXiv2008

Toric varieties - degenerations and fundamental groups

In this paper we calculate fundamental groups (and some of their quotients) of complements of four toric varieties branch curves. For these calculations, we study properties and degenerations of these toric varieties and the braid monodromies of the branch curves in $\mathbb{CP}^2$. The fundamental groups related to the first three toric varieties turn to be quotients of the Artin braid groups $\mathcal{B}_5$, $\mathcal{B}_6$, and $\mathcal{B}_4$, while the fourth one is a certain quotient of the group $\tilde{\mathcal{B}}_6 = \mathcal{B}_6/<[X,Y]>$, where $X, Y$ are transversal. The quotients of all four groups by the normal subgroups generated by the squares of the standard generators are respectively $S_5, S_6, S_4$ and $S_6$. We therefore conclude that the fundamental groups of the Galois covers of the four given toric varieties are all trivial.

math.GT↗

arXiv2007

Fundamental groups of some special quadric arrangements

In this work we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in $\mathbb{P}^2$. The first arrangement is a union of $n$ quadrics, which are tangent to each other at two common points. The second arrangement is composed of $n$ quadrics which are tangent to each other at one common point. The third arrangement is composed of $n$ quadrics, $n-1$ of them are tangent to the $n$'th one and each one of the $n-1$ quadrics is transversal to the other $n-2$ ones.

math.AG↗

arXiv2001

Oblique Surface Waves on a Pair of Planar Periodic Slotted Waveguides

The dispersion relation and mode amplitudes of oblique surface waves propagating on an acoustic double comb filter are obtained with a method based on the calculus of residues. We obtain a better agreement (below 480 Hz) between theoretical predictions and measurements reported previously when the filter was being supposed to be made of a single comb structure.

physics.class-ph↗