Related papers: Equisingular Deformations of Legendrian Curves
We consider evolution equations for curves in the 3-dimensional sphere $S^3$ that are invariant under the group $SU(2,1)$ of pseudoconformal transformations, which preserves the standard contact structure on the sphere. In particular, we…
This paper studies the obstructions to deforming a map from a complex variety to another variety which is an immersion of codimension one. We extend the classical notion of semiregularity of subvarieties to maps between varieties, and show…
Real Legendrian subvarieties are classical objects of differential geometry and classical mechanics and they have been studied since antiquity. However, complex Legendrian subvarieties are much more rigid and have more exceptional…
We construct universal local deformations (Kuranishi families) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the…
We study deformations of plane curves in the similarity geometry. It is known that continuous deformations of smooth curves are described by the Burgers hierarchy. In this paper, we formulate the discrete deformation of discrete plane…
We prove that an inverse semigroup over an Adian presentation is E-unitary.
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
In this paper, we focus on some characterizations for curves in the Galilean and Pseudo-Galilean space.
We embed several copies of the derived category of a quiver and certain line bundles in the derived category of an associated moduli space of representations, giving the start of a semiorthogonal decomposition. This mirrors the…
The deformation theory of curves is studied by using the canonical ideal. The problem of lifting curves with automorphisms is reduced to a lifting problem of linear representations.
This is a survey paper on Legendrian and transversal knots for Handbook of Knot Theory.
We construct pairs of elliptic curves over number fields with large intersection of projective torsion points.
We determine endomorphism algebras of abelian surfaces with quaternion multiplication.
The aim of this paper is to give some characterizations for N-Legendre and N-slant curves in the unit tangent bundles of surfaces endowed with natural diagonal lifted structures.
We construct new special Lagrangian submanifolds in complex Euclidean space using a pair of minimal Legendrian submanifolds in odd-dimensional spheres and certain Lagrangian surface belonging to a family that can be considered as a…
We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in the families of Legendre, Jacobi, Hessian and generalized Hessian curves.
This paper gives various methods for constructing vector bundles over elliptic curves and more generally over families of elliptic curves. We construct universal families over generalized elliptic curves via spectral cover methods and also…
We introduce the notion of noncommutative equiangular lines and derive noncommutative versions of fundamental van Lint-Seidel relative and Gerzon universal bounds.
We give more or less explicit equations for all two-dimensional cusp singularities of embedding dimension at least 4. They are closely related to Felix Klein's equations for universal curves with level n structure. The main technical result…
We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…