Related papers: Arithmetic properties of homogeneous Hilbert curve…
Recent work of Schenck, Stillman and Yuan arXiv:2011.10871 outlines all possible Betti tables for Artin Gorenstein algebras $A$ with regularity($A$) = 4 = codim($A$). We populate the second half of this list with examples of stable curves,…
We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape…
: Algebraic properties of orbifold models on arbitrary Riemann surfaces are investigated. The action of mapping class group transformations and of standard geometric operations is given explicitly. An infinite dimensional extension of the…
We provide an algorithm of constructing a rectifiable curve between two sufficiently close points of a proximally smooth set in a uniformly convex and uniformly smooth Banach space. Our algorithm returns a reasonably short curve between two…
We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as…
The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…
In this paper we introduce an effective method to construct rational deformations between couples of Borel-fixed ideals. These deformations are governed by flat families, so that they correspond to rational curves on the Hilbert scheme.…
We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.
The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection.…
The purpose of this article is to find a family of curves parametrized by arc length and that depend on an angular function and an intrinsic fraction function, which is defined as the quotient between torsion and curvature. We find for this…
A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.
We define refined invariants which "count" nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces.…
A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of $f$. Since its introduction, numerous…
In this paper, we discuss some problems of elementary plane differential geometry and kinematics. Although the results are not new, the consistent use of complex-valued functions (plane curves) of a real variable (parameter) allows to…
We review some basic concepts related to convex real projective structures from the differential geometry point of view. We start by recalling a Riemannian metric which originates in the study of affine spheres using the Blaschke connection…
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with…
We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…
This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes…
The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…