Related papers: Projective isomorphisms between rational surfaces
We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification…
A general strategy is given for the classification of graphs of rational surface singularities. For each maximal rational double point configuration we investigate the possible multiplicities in the fundamental cycle. We classify completely…
The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…
We determine those maps between affine or projective spaces that are linear in the abstract sense of transforming collinear points into collinear points and whose restriction to any line is constant or injective. Our results are extensions…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…
The classification of minimal rational surfaces and the birational links between them by Iskovskikh, Manin and others is a well-known subject in the theory of algebraic surfaces. We explain algorithms that realise links of type II between…
A deterministic method for synthesizing the interconnect topologies optimized for the required properties is proposed. The method is based on the original description of graphs by projections, on establishing the bijective correspondence of…
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
We count by height the number of elliptic curves over the rationals, both up to isomorphism over the rationals and over an algebraic closure thereof, that admit a cyclic isogeny of degree $7$.
This note derives parametrizations for surfaces of revolution that satisfy an affine-linear relation between their respective curvature radii. Alongside, parametrizations for the uniform normal offsets of those surfaces are obtained. Those…
The degree of irrationality of a smooth projective variety $X$ is the minimal degree of a dominant rational map $X\dashrightarrow \mathbb{P}^{\dim X}$. We show that if an abelian surface $A$ over $\mathbb{C}$ is such that the image of the…
We establish a couple of dynamical properties of surjective rational maps $f: X \dashrightarrow X$ for smooth projective surfaces $X$. We also give a numerical characterization of regular $f$ in the case when $X$ is a del Pezzo surface.…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
We classify two dimensional integrable mappings by investigating the actions on the fiber space of rational elliptic surfaces. While the QRT mappings can be restricted on each fiber, there exist several classes of integrable mappings which…
In this paper we develop the formalism of rational complex Bezier curves. This framework is a simple extension of the CAD paradigm, since it describes arc of curves in terms of control polygons and weights, which are extended to complex…
We use twisted stable maps to compute the number of rational degree d plane curves having prescribed contacts to a smooth plane cubic.
We study smooth rational closed embeddings of the real affine line into the real affine plane, that is algebraic rational maps from the real affine line to the real affine plane which induce smooth closed embeddings of the real euclidean…
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…
We combine the newly discovered technique, which computes explicit formulas for the image of an algebraic curve under rational transformation, with techniques that enable to compute braid monodromies of such curves. We use this combination…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…