Related papers: A Construction to find any Circle through a Given …
The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by Griffiths-Green to solve the problem.
Starting with a flat sheet of paper, points can be constructed as the intersection of two folds. The set of constructible points clearly depends on which folds are admissible. In this paper, we study the situation where a fold is admissible…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
It is well known that a center of a given circle cannot be constructed using only a straightedge and that this was proven by David Hilbert. Still it is not so clear what kind of object is proven to be non-existing. We analyze different…
This version is similar to math.CO/0210113. We've changed Conjectures 1.1 and 1.2 so that they cover arbitrary graphs(digraphs). Let G be an arbitrary graph(digraph). Then - in polynomial time - either an algorithm obtains a hamilton…
In this note we prove that the centers of a closed chain of circles for which every two consecutive members meet in the points of two given circles form a tangent polygon of a conic.
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers.
The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is established. An algorithm for constructing a Hamiltonian cycle…
In this short note we use the notion of power structure over the Grothendieck ring of complex algebraic varieties to study generating series of classes of Hilbert schemes of points on complex orbifolds.
In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…
A Hamilton cycle in a digraph is a cycle that passes through all the vertices, where all the arcs are oriented in the same direction. The problem of finding Hamilton cycles in directed graphs is well studied and is known to be hard. One of…
It is well known that several classical geometry problems (e.g., angle trisection) are unsolvable by compass and straightedge constructions. But what kind of object is proven to be non-existing by usual arguments? These arguments refer to…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
We prove that every pointed closed convex set in $\mathbb{R}^n$ is the intersection of all the rational closed halfspaces that contain it. This generalizes a previous result by the authors for compact convex sets.
I provide methods of constructing elliptic and hyperelliptic curves over global fields with interesting rational points over the given fields or over large field extensions. I also provide a elliptic curves defined over any given number…
We showed in another paper [arXiv:1103.1759] that every connected graph can be realized as the cut locus of some point on some riemannian surface $S$. Here, criteria for the orientability of $S$ are given, and are applied to classify the…
We consider closed chains of circles $C_1,C_2,\ldots,C_n,C_{n+1}=C_1$ such that two neighbouring circles $C_i,C_{i+1}$ intersect or touch each other with $A_i$ being a common point. We formulate conditions such that a polygon with vertices…
In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.
A closed-form solution for the boundary of the flat state of an orthogonal cross section of contiguous surface geometry formed by the intersection of two cylinders of equal radii oriented in dual directions of rotation about their…