Configuration spaces and limits of Voronoi diagrams (2009)
Roderik Lindenbergh, Dirk Siersma
The Voronoi diagram of n distinct generating points divides the plane into cells, each of which consists of points most close to one particular generator. After introducing ‘limit Voronoi diagrams...
POLISH ACADEMY OF SCIENCES WARSZAWA 199* PROPERTIES OF CONFLICT SETS IN THE PLANE (2008)
Abstract. This paper studies the smoothness and the curvature of con ict sets of the distance function in the plane. Con ict sets are also well known as 'bisectors'. We prove smoothness in...
The Nine Morse Generic Tetrahedra (2008)
Siersma, Dirk, Van Manen, Martijn
There are two types of shapes for a generic triangle-acute and obtuse. These shapes are also distinguished by the (topological) Morse theory of the minimal distance function to the vertices. We can...
Configuration spaces and limits of Voronoi diagrams (2008)
Roderik Lindenbergh, Dirk Siersma
Abstract The Voronoi diagram of n distinct generating points divides theplane into cells, each of which consists of points most close to one
Singularity Exchange at Infinity (2008)
Abstract. In families of polynomial functions one may encounter “singularity exchange at infinity ” when singular points escape from the space and produce “virtual ” singularities of the...
Deformations of polynomials, boundary singularities and monodromy (2008)
Dedicated to Vladimir Igorevich Arnol’d on the occasion of his 65th anniversary Abstract. We study the topology of polynomial functions by deforming them generically. We explain how the...
CURVATURE AND GAUSS-BONNET DEFECT OF GLOBAL AFFINE HYPERSURFACES (2008)
Abstract. The total curvature of complex hypersurfaces in C n+1 and its variation in families appear to depend not only on singularities but also on the behaviour in the neighbourhood of infinity. We...
LINES ON BRIESKORN-PHAM SURFACES (2008)
Guangfeng Jiang, Mutsuo Oka, Duc Tai Pho, Dirk Siersma
Abstract. By using toric modifications and a result of Gonzalez-Sprinberg and Lejeune-Jalabert, we answer the following questions completely. On which Brieskorn-Pham surface there exist smooth curves...
! C be a polynomial function. We define global polar invariants associated to fibres of f and we describe a CW-complex model of a fibre. We show how to use affine polar curves in order to study the...
The Vanishing Topology of Non Isolated Singularities (2007)
We consider non-zero holomorphic function germs f: (C
polynomials of degree 4 in two variables (2007)
Classification of singularities at infinity of
Universidade Federal de Goi'as (2007)
Jorge Sotomayor, Dirk Siersma, Mathematisch Instituut, Ronaldo Garcia
Instituto de Matem'atica e Estat'istica
POLISH ACADEMY OF SCIENCES WARSZAWA 199* PROPERTIES OF CONFLICT SETS IN THE PLANE (2007)
Abstract. This paper studies the smoothness and the curvature of conflict sets of the distance function in the plane. Conflict sets are also well known as 'bisectors'. We prove smoothness...
Vanishing cycles and singularities of meromorphic functions (2007)
We study vanishing cycles of meromorphic functions. This gives a new and unitary point of view, extending the study of the topology of holomorphic germs-- as initiated by Milnor in the sixties-- and...
! C be any polynomial function. By using global polar methods, we introduce models for the fibers of f and we study the monodromy at atypical values of f, including the value infinity. We construct a...
Deformations of polynomials, boundary singularities and monodromy (2007)
Dedicated to Vladimir Igorevich Arnol'd on the occasion of his 65th anniversary Abstract. We study the topology of polynomial functions by deforming them generically. We explain how the...
Metric Properties of Conflict Sets (2007)
In this paper we show that the tangent cone of a conflict set in $R^n$ is a linear affine cone over a conflict set of smaller dimension and has dimension $n-1$. Moreover we give an example where the...
Curvature and Gauss-Bonnet defect of global affine hypersurfaces (2006)
The total curvature of complex hypersurfaces in $\bC^{n+1}$ and its variation in families appear to depend not only on singularities but also on the behaviour in the neighbourhood of infinity. We...
Singularity exchange at the frontier of the space (2006)
In deformations of polynomial functions one may encounter ``singularity exchange at infinity'' when singular points disappear from the space and produce ``virtual'' singularities which have an...
Deformations of polynomials, boundary singularities and monodromy (2006)
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related...
Power diagrams and their applications (2005)
Van Manen, Martijn, Siersma, Dirk
We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. Our concept of a Morse poset generalizes to power...
Curvature and Gauss-Bonnet defect of global affine hypersurfaces (2004)
The total curvature of complex hypersurfaces in $\bC^{n+1}$ and its variation in families appear to depend not only on singularities but also on the behaviour in the neighbourhood of infinity. We...
Singularity exchange at the frontier of the space (2004)
In deformations of polynomial functions one may encounter ``singularity exchange at infinity'' when singular points disappear from the space and produce ``virtual'' singularities which have an...
CONFIGURATION SPACES AND LIMITS OF VORONOI DIAGRAMS (2004)
Banach Center Publications, Roderik Lindenbergh, Dirk Siersma
Abstract. The Voronoi diagram of n distinct generating points divides the plane into cells, each of which consists of points most close to one particular generator. After introducing ‘limit Voronoi...
Deformations of polynomials, boundary singularities and monodromy (2002)
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related...
Extensible Graph Markup and Modeling Language). http://www.cs.rpi.edu/ ~puninj/XGMML (2001)
Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.
Vanishing cycles and singularities of meromorphic functions (1999)
We study vanishing cycles of meromorphic functions. This gives a new and unitary point of view, extending the study of the topology of holomorphic germs -- as initiated by Milnor in the sixties --...
Voronoi Diagrams and Morse Theory of the Distance Function (1999)
We consider the (minimal) distance function of a point in the plane to a set P of N points in the plane. The locus of non-di erentiability of this distance function consists (besides of the points of...
Voronoi Diagrams and Morse Theory of the Distance Function (1999)
We consider the (minimal) distance function of a point in the plane to a set P of N points in the plane. The locus of non-differentiability of this distance function consists (besides of the points...
Curvatures of Conflict Surfaces in Euclidean 3-Space (1999)
Jorge Sotomayor, Dirk Siersma, Mathematisch Instituut, Ronaldo Garcia
This article extends to three dimensions results on the curvature of the conflict curve for pairs of convex sets of the plane, established by Siersma [3]. In the present case a conflict surface...
Classification and deformation of singularities / (1974)
Proefschrift Universiteit van Amsterdam.
Singularities at Infinity and Their Vanishing Cycles
We study the topology of the fibres of polynomials f with "singularities at infinity ". We first define W-singularities at infinity, where W refers to a certain Whitney stratification on...
Singularities at infinity and their vanishing cycles, II. Monodromy
Let f : C n ! C be any polynomial function. By using global polar methods, we introduce models for the fibers of f and we study the monodromy at atypical values of f , including the value infinity....