The braid monodromy factorization of the branch curve of a surface of general type is known to be... more The braid monodromy factorization of the branch curve of a surface of general type is known to be an invariant that completely determines the diffeomorphism type of the surface. Calculating this factorization is of high technical complexity; computing the braid monodromy factorization of branch curves of surfaces uncovers new facts and invariants of the surfaces. Since finding the branch curve of a surface is very difficult, we degenerate the surface into a union of planes. Thus, we can find the braid monodromy of the branch curve of the degenerated surface, which is a union of lines. The regeneration of the singularities of the branch curve, studied locally, leads us to find the global braid monodromy factorization of the branch curve of the original surface. So far, only the regeneration of the BMF of 3,4 and 6-point (a singular point which is the intersection of 3 / 4 / 6 planes) were done. In this paper, we fill the gap and find the braid monodromy of the regeneration of a 5-poi...
This paper presents a new subdivision scheme that operates over an infinite triangulation, which ... more This paper presents a new subdivision scheme that operates over an infinite triangulation, which is regular except for a single extraordinary vertex. The scheme is based on the quartic three-directional Box-spline scheme, and is guaranteed to generate C2 limit functions whenever the valency n of the extraordinary vertex is in the range 4⩽n⩽20. The new scheme differs from the commonly
We present a novel approach for three-dimensional (3D) measurements that includes the projection ... more We present a novel approach for three-dimensional (3D) measurements that includes the projection of coherent light through ground glass. Such a projection generates random speckle patterns on the object or on the camera, depending if the configuration is transmissive or reflective. In both cases the spatially random patterns are seen by the sensor. Different spatially random patterns are generated at different planes. The patterns are highly random and not correlated. This low correlation between different patterns is used for both 3D mapping of objects and range finding.
We list all the possible fundamental groups of the complements of real conic-line arrangements wi... more 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
In this article, we compute the braid monodromy of two algebraic curves defined over R. These two... more 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 C2 and
In this article we construct a specific projective degeneration of K3 surfaces of degree 2g-2 in ... more In this article we construct a specific projective degeneration of K3 surfaces of degree 2g-2 in P^g to a union of 2g-2 planes, which meet in such a way that the combinatorics of the configuration of planes is a triangulation of the 2-sphere. Abstractly, such degenerations are said to be Type III degenerations of K3 surfaces. Although the birational geometry
Given a system of equations in a “random” finitely generated subgroup of the braid group, we show... more Given a system of equations in a “random” finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability. Moreover, with a significant probability, the solution will be the first in the list. This gives a probabilistic solution to:
... Boris Moishezon Mina Teicher ... following types: a 1, a 2, b, c, as follows: at: a branch po... more ... Boris Moishezon Mina Teicher ... following types: a 1, a 2, b, c, as follows: at: a branch point, top equivalent to y2 _ x = 0 a2: a branch point, top equivalent to y2 + x = 0 b: a tangent point, top equivalent to y(y - x 2) = 0 c: intersection of m nonsingular branches of C, transversal to ...
In this paper we prove that the Hirzebruch surface F2,(2,2) embedded in CP17 supports the conject... more In this paper we prove that the Hirzebruch surface F2,(2,2) embedded in CP17 supports the conjecture on the structure and properties of fundamental groups of complement of branch curves of generic projections, as laid out in [M. Teicher, New Invariants for surfaces, Contemp. Math. 231 (1999) 271–281]. We use the regeneration from [M. Friedman, M. Teicher, The regeneration of a
Given a projective surface and a generic projection to the plane, the braid monodromy factorizati... more Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants ((10)), stable on deforma- tions. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in C2
We discuss the applications of fundamental groups (of complements of curves) computations (and po... more We discuss the applications of fundamental groups (of complements of curves) computations (and possibly the computations of the second homotopy group as a model over it) to the classification of algebraic surface. We prove that the fundamental group of the complement of the branch curve of a generic projection of a Veronese surface to the complex plane is an "almost solvable" group in the sense that it contains a solvable group of finite index and thus we can consider the second fundamental group as model over the first.
The braid monodromy factorization of the branch curve of a surface of general type is known to be... more The braid monodromy factorization of the branch curve of a surface of general type is known to be an invariant that completely determines the diffeomorphism type of the surface. Calculating this factorization is of high technical complexity; computing the braid monodromy factorization of branch curves of surfaces uncovers new facts and invariants of the surfaces. Since finding the branch curve of a surface is very difficult, we degenerate the surface into a union of planes. Thus, we can find the braid monodromy of the branch curve of the degenerated surface, which is a union of lines. The regeneration of the singularities of the branch curve, studied locally, leads us to find the global braid monodromy factorization of the branch curve of the original surface. So far, only the regeneration of the BMF of 3,4 and 6-point (a singular point which is the intersection of 3 / 4 / 6 planes) were done. In this paper, we fill the gap and find the braid monodromy of the regeneration of a 5-poi...
This paper presents a new subdivision scheme that operates over an infinite triangulation, which ... more This paper presents a new subdivision scheme that operates over an infinite triangulation, which is regular except for a single extraordinary vertex. The scheme is based on the quartic three-directional Box-spline scheme, and is guaranteed to generate C2 limit functions whenever the valency n of the extraordinary vertex is in the range 4⩽n⩽20. The new scheme differs from the commonly
We present a novel approach for three-dimensional (3D) measurements that includes the projection ... more We present a novel approach for three-dimensional (3D) measurements that includes the projection of coherent light through ground glass. Such a projection generates random speckle patterns on the object or on the camera, depending if the configuration is transmissive or reflective. In both cases the spatially random patterns are seen by the sensor. Different spatially random patterns are generated at different planes. The patterns are highly random and not correlated. This low correlation between different patterns is used for both 3D mapping of objects and range finding.
We list all the possible fundamental groups of the complements of real conic-line arrangements wi... more 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
In this article, we compute the braid monodromy of two algebraic curves defined over R. These two... more 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 C2 and
In this article we construct a specific projective degeneration of K3 surfaces of degree 2g-2 in ... more In this article we construct a specific projective degeneration of K3 surfaces of degree 2g-2 in P^g to a union of 2g-2 planes, which meet in such a way that the combinatorics of the configuration of planes is a triangulation of the 2-sphere. Abstractly, such degenerations are said to be Type III degenerations of K3 surfaces. Although the birational geometry
Given a system of equations in a “random” finitely generated subgroup of the braid group, we show... more Given a system of equations in a “random” finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability. Moreover, with a significant probability, the solution will be the first in the list. This gives a probabilistic solution to:
... Boris Moishezon Mina Teicher ... following types: a 1, a 2, b, c, as follows: at: a branch po... more ... Boris Moishezon Mina Teicher ... following types: a 1, a 2, b, c, as follows: at: a branch point, top equivalent to y2 _ x = 0 a2: a branch point, top equivalent to y2 + x = 0 b: a tangent point, top equivalent to y(y - x 2) = 0 c: intersection of m nonsingular branches of C, transversal to ...
In this paper we prove that the Hirzebruch surface F2,(2,2) embedded in CP17 supports the conject... more In this paper we prove that the Hirzebruch surface F2,(2,2) embedded in CP17 supports the conjecture on the structure and properties of fundamental groups of complement of branch curves of generic projections, as laid out in [M. Teicher, New Invariants for surfaces, Contemp. Math. 231 (1999) 271–281]. We use the regeneration from [M. Friedman, M. Teicher, The regeneration of a
Given a projective surface and a generic projection to the plane, the braid monodromy factorizati... more Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants ((10)), stable on deforma- tions. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in C2
We discuss the applications of fundamental groups (of complements of curves) computations (and po... more We discuss the applications of fundamental groups (of complements of curves) computations (and possibly the computations of the second homotopy group as a model over it) to the classification of algebraic surface. We prove that the fundamental group of the complement of the branch curve of a generic projection of a Veronese surface to the complex plane is an "almost solvable" group in the sense that it contains a solvable group of finite index and thus we can consider the second fundamental group as model over the first.
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Papers by Mina Teicher