76 citations · 542 across the 72 of their papers we have counts for
32 papers · 1 filter
Phylogenetic Trees and the Moduli Space of n Points on the Projective Line
Herwig Hauser, Jiayue Qi, Josef Schicho
This is an expository paper. The geometry of phylogenetic trees is used to present in an accessible and pleasant fashion the results of Deligne, Mumford, and Knudsen about the modu…
How to Reconstruct a Planar Map From its Branching Curve
Eriola Hoxhaj, Josef Schicho
We present an algorithm for constructing a map with a given branching curve. The stepping stone is the ramification curve, which is obtained as the li…
Using Algebraic Geometry to Reconstruct a Darboux Cyclide from a Calibrated Camera Picture
Eriola Hoxhaj, Jean Michel Menjanahary, Josef Schicho
The task of recognizing an algebraic surface from a single apparent contour can be reduced to the recovering of a homogeneous equation in four variables from its discriminant. In t…
Tri-linear birational maps in dimension three
Laurent Busé, Pablo González-Mazón, Josef Schicho
A tri-linear rational map in dimension three is a rational map defined by four tri-linear polynomials witho…
Hexapods with a small linear span
Hans-Christian Graf von Bothmer, Matteo Gallet, Josef Schicho
The understanding of mobile hexapods, i.e., parallel manipulators with six legs, is one of the driving questions in theoretical kinematics. We aim at contributing to this understan…
Projective isomorphisms between rational surfaces
Bert Jüttler, Niels Lubbes, Josef Schicho
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of…
On the multihomogeneous Bézout bound on the number of embeddings of minimally rigid graphs
Evangelos Bartzos, Ioannis Z. Emiris, Josef Schicho
Rigid graph theory is an active area with many open problems, especially regarding embeddings in or other manifolds, and tight upper bounds on their number for a giv…
Reconstruction of surfaces with ordinary singularities from their silhouettes
Matteo Gallet, Niels Lubbes, Josef Schicho +1
We present algorithms for reconstructing, up to unavoidable projective automorphisms, surfaces with ordinary singularities in three dimensional space starting from their silhouette…
An application of Bertini Theorem
Mehdi Makhul, Josef Schicho
Given an irreducible variety over a finite field, the density of hypersurfaces of varying degree intersecting in an irreducible subvariety is , by a result of Charle…
Kinematic generation of Darboux cyclides
Niels Lubbes, Josef Schicho
We state a relation between two families of lines that cover a quadric surface in the Study quadric and two families of circles that cover a Darboux cyclide.
Counting projections of rational curves
Matteo Gallet, Josef Schicho
Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of t…
The number of realizations of a Laman graph
Jose Capco, Matteo Gallet, Georg Grasegger +3
Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph…
On a conjecture of Tian
Hamid Abban, Ivan Cheltsov, Josef Schicho
We study Tian's -invariant in comparison with the -invariant for pairs consisting of a smooth surface of degree in the projective three-dimensional spac…
Ambiguities in a Problem in Planar Geodesy
Josef Schicho, Matteo Gallet
This is a study of a problem in geodesy with methods from complex algebraic geometry: for a fixed number of measure points and target points at unknown position in the Euclidean pl…
Möbius Photogrammetry
Matteo Gallet, Georg Nawratil, Josef Schicho
Motivated by results on the mobility of mechanical devices called pentapods, this paper deals with a mathematically freestanding problem, which we call Möbius Photogrammetry. Unlik…
A Simplified Game for Resolution of Singularities
Josef Schicho
We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strateg…
The Theory of Bonds II: Closed 6R Linkages with Maximal Genus
Gábor Hegedüs, Zijia Li, Josef Schicho +1
In this paper, we introduce a method that allows to produce necessary conditions on the Denavit--Hartenberg parameters for the mobility of a closed linkage with six rotational join…
An inequality for adjoint rational surfaces
Christian Haase, Josef Schicho
We generalize an inequality for convex lattice polygons -- aka toric surfaces -- to general rational surfaces.
Computational aspects of gonal maps and radical parametrization of curves
Josef Schicho, Frank-Olaf Schreyer, Martin Weimann
We develop in this article an algorithm that, given a projective curve , computes a \textit{gonal map}, that is, a finite morphism from to the projective line of minimal deg…
Classification of Angle-Symmetric 6R Linkage
Zijia Li, Josef Schicho
In this paper, we consider a special kind of overconstrained 6R closed linkages which we call angle-symmetric 6R linkages. These are linkages with the property that the rotation an…
The Theory of Bonds: A New Method for the Analysis of Linkages
Gábor Hegedüs, Josef Schicho, Hans-Peter Schröcker
In this paper we introduce a new technique, based on dual quaternions, for the analysis of closed linkages with revolute joints: the theory of bonds. The bond structure comprises a…
Effective radical parametrization of trigonal curves
Josef Schicho, David Sevilla
Let be a non-hyperelliptic algebraic curve. It is known that its canonical image is the intersection of the quadrics that contain it, except when is trigonal (that is, it h…
Deciding trigonality of algebraic curves
Josef Schicho, David Sevilla
Let C be a non-hyperelliptic algebraic curve of genus at least 3. Enriques and Babbage proved that its canonical image is the intersection of the quadrics that contain it, except w…
Lattice polygons and families of curves on rational surfaces
Niels Lubbes, Josef Schicho
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more ge…