Related papers: Projective Line Revisited
In this paper we present an extension of the classical Root-Locus (RL) method where the points are calculated in the real projective plane instead of the conventional affine real plane; we denominate this extension of the Root-Locus as…
We reprove the strong Hanani-Tutte theorem on the projective plane. In contrast to the previous proof by Pelsmajer, Schaefer and Stasi, our method is constructive and does not rely on the characterization of forbidden minors, which gives…
This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.
We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
The group of piecewise projective homeomorphisms of the line provides straightforward counter-examples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean…
In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.
A complex projective manifold is rationally connected, resp. rationally simply connected, if finite subsets are connected by a rational curve, resp. the spaces parameterizing these connecting rational curves are themselves rationally…
This paper aims to develop a theory of projective and affine structures on higher-dimensional varieties in positive characteristic. This theory deals with Frobenius-projective and Frobenius-affine structures, which have been previously…
We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.
Given a collection of points in the plane, classifying which subsets are collinear is a natural problem and is related to classical geometric constructions. We consider collections of points in a projective plane over a finite field such…
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
Over the complex numbers, there are 92 plane conics meeting 8 general lines in projective 3-space. Using the Euler class and local degree from motivic homotopy theory, we give an enriched version of this result over any perfect field. This…
We focus on a branch of region-based spatial logics dealing with affine geometry. The research on this topic is scarce: only a handful of papers investigate such systems, mostly in the case of the real plane. Our long-term goal is to…
Generalizations of the classical affine Lelieuvre formula to surfaces in projective three-dimensional space and to hypersurfaces in multi- dimensional projective space are given. A discrete version of the projective Lelieuvre formula is…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
We give a short, elementary and explicit proof of the existence of Hilbert schemes of points on affine schemes. As a direct consequence we obtain the existence of the Hilbert scheme of points on any projective scheme, not necessarily of…
In a previous paper, we provided some update in the treatment of the finiteness theorem for rational maps of finite degree from a fixed variety to varieties of general type. In the present paper we present another improvement, introducing…