On the Variety of Smooth Rational Space Curves with Given Degree and Normal Bundle.
On the variety of special linear systems on an algebraic curve.
On torsion points on an elliptic curves via division polynomials.
On translation invariance for Wrd.
On triple curves through a rational triple point of a surface
Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.
On universal elliptic curves over Igusa curves.
On valued function fields II. Regular functions and elements with the uniqueness property.
On valued function fields III. Reductions of algebraic curves.
On vanishing inflection points of plane curves
We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs which take into account the inflection points of the fibres of . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.
On x³ + y³ + z³ = 3μxyz and Jacobi polynomials
On Zariski's theorem in positive characteristic
In the current paper we show that the dimension of a family of irreducible reduced curves in a given ample linear system on a toric surface over an algebraically closed field is bounded from above by , where denotes a general curve in the family. This result generalizes a famous theorem of Zariski to the case of positive characteristic. We also explore new phenomena that occur in positive characteristic: We show that the equality does not imply the nodality of even if belongs to the...
One attempt to the modular function - II
One-dimensional Hurwitz spaces, modular curves, and real forms of Belyi meromorphic functions.
One-Dimensional Local Rings with Reduced Associated Graded Ring and Their Hilbert Functions.
Operads and algebraic geometry.
Opérateurs différentiels et courbes elliptiques
Operations of Points on Elliptic Curve in Projective Coordinates
In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compellProjCo and addellProjCo are unary and binary operations of a point over the elliptic curve.
Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.
We study a constructive method to find an algebraic curve in the real projective plane with a (possibly singular) topological type given in advance. Our method works if the topological model T to be realized has only double singularities and gives an algebraic curve of degree 2N+2K, where N and K are the numbers of double points and connected components of T. This degree is optimal in the sense that for any choice of the numbers N and K there exist models which cannot be realized algebraically with...
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface (II).
In [6], orbifold G-bundles on a certain class of elliptic fibrations over a smooth complex projective curve X were related to parabolic G-bundles over X. In this continuation of [6] we define and investigate holomorphic connections on an orbifold G-bundle over an elliptic fibration.
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.
Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights at any...