Related papers: Affine monomial curves
For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.
We study arithmetic properties of tangent cones associated to affine monomial curves, using the concept of gluing. In particular we characterize the Cohen-Macaulay and Gorenstein properties of tangent cones of some families of monomial…
Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
We give a survey of the theory of affine spheres, emphasizing the convex cases and relationsships to Monge-Ampere equations and geometric structures on manifolds.
We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli…
Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of…
We consider log deformations of affine surfaces with fibrations by the affine lines. Such a fibration is of affine type (resp. of complete type) if the base curve of the fibration is an affine curve (resp. a complete curve). The case of…
In this work we study the affine principal lines of surfaces in 3-space. We consider the binary differential equation of the affine curvature lines and obtain the topological models of these curves near the affine umbilic points (elliptic…
The aim of this paper is to provide an explicit basis of the miniversal deformation of a monomial curve defined by a free semigroup -- these curves make up a notable family of complete intersection monomial curves. First, we dispense a…
This paper is devoted to the complete classification of space curves under affine transformations in the view of Cartan's theorem. Spivak has introduced the method but has not found the invariants. Furthermore, for the first time, we…
A well-known and difficult problem in computational number theory and algebraic geometry is to write down equations for branched covers of algebraic curves with specified monodromy type. In this article, we present a technique for computing…
Our aim in this paper is to compute the Poincar\'{e} series of the derivation module of the projective closure of certain affine monomial curves.
This is a survey paper dealing with moduli aspects of curves over finite fields. It discusses counting points of moduli spaces, relations with modular forms and stratifications on moduli spaces.
In this paper, we consider affine self-similar solutions for the affine curve shortening flow in the Euclidean plane. We obtain the equations of all affine self-similar solutions up to affine transformations and solve the equations or give…
We explicitly construct the algebraic model of affine Jacobian of a generic algebraic curve of high genus and use it to compute the Euler characteristic of the Jacobian and investigate its structure.
We give an overview of the affine surface area, its properties and its history.
We study the distribution of algebraic points on curves in abelian varieties over finite fields.
We survey and investigate some computational aspects of the Fourier-Mukai transform.
We establish several compatibility results between residue maps in \'etale and Galois cohomology that arise naturally in the analysis of smooth affine algebraic curves having good reduction over discretely valued fields. These results are…