Related papers: Covering Rational Ruled Surfaces
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar case. As for space…
We give upper bounds for the number of rational points of bounded anti-canonical height on del Pezzo surfaces of degree at most five over any global field whose characteristic is not equal to two or three. For number fields these results…
This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with…
The purpose of this paper is to explore the question "to what extent could we produce formal, machine-verifiable, proofs in real algebraic geometry?" The question has been asked before but as yet the leading algorithms for answering such…
We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for…
We present an integrability criterion for rational mappings based on two requirements. First, that a given point should have a unique preimage under the mapping and, second, that the spontaneously appearing singularities be confined to a…
This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…
It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance $\epsilon>0$ and an $\epsilon$-irreducible algebraic affine plane curve $\mathcal C$ of…
Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…
We propose a novel method to generate a small set of ruled surfaces that do not collide with the input shape for linear hot-wire rough machining. Central to our technique is a new observation: the ruled surfaces constructed by vertical…
We give an algorithm that, for a given value of the geometric genus $p_g,$ computes all regular product-quotient surfaces with abelian group that have at most canonical singularities and have canonical system with at most isolated base…
We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…
We construct a smooth complex projective rational surface with infinitely many mutually non-isomorphic real forms. This gives the first definite answer to a long standing open question if a smooth complex projective rational surface has…
Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of…
In this paper we present an algorithm for computing a matrix representation for a surface in P^3 parametrized over a 2-dimensional toric variety T. This algorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it was implemented in…
Results of number of geometric operations (often used in technical practise, as e.g. the operation of blending) are in many cases surfaces described implicitly. Then it is a challenging task to recognize the type of the obtained surface,…
We study unirationality of a Del Pezzo surface of degree two over a given (non algebraically closed) field, under the assumption that it admits at least one rational double point over an algebraic closure of the base field. As corollaries…
We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our…
We utilise the two principles of decoupling introduced in [arXiv:2407.16108] to prove decoupling for two types of surfaces exhibiting radial symmetry. The first type are surfaces of revolution in $\mathbb R^n$ generated by smooth surfaces…
In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.