Related papers: Integrable Deformations of Algebraic Curves
We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
In this paper, we investigate the possibility of constructing isomonodromic deformations of logarithmic connections on curves by using ramified covers. We give new examples and prove a classification result.
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…
The purpose of this note is to extend the divergences analyzed in a previous work by application of the Deformed Logarithm in its most general form. In a study on entropic divergences, we have analyzed the different forms of the deformed…
Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…
We consider versal deformations of 0|3-dimensional L-infinity algebras, which correspond precisely to ordinary (non-graded) three dimensional Lie algebras. The classification of such algebras over C is well known, although we shall give a…
We study the symmetry groups and winding numbers of planar curves obtained as images of weighted sums of exponentials. More generally, we study the image of the complex unit circle under a finite or infinite Laurent series using a…
An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.
Planar curves with periodically varying curvature arise in the natural sciences as the result of a wide variety of periodic processes. The total curvature of a periodic arc in such curves constrains their symmetry. It is shown how the total…
Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systInterpretation of dispersionless integrable hierarchies as equations…
The paper is devoted to differential geometric invariants determining a Frenet curve in up to a direct similarity These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then,…
In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields…
We identify the algebra of regular functions on the space of quartic polynomials in three complex variables invariant under SL(3,C) with an algebra of meromorphic automorphic forms on the complex 6-ball. We also discuss the underlying…
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…
We study non-trivial deformations of the natural action of the Lie algebra $\mathrm{Vect}({\mathbb R}^n)$ on the space of differential forms on ${\mathbb R}^n$. We calculate abstractions for integrability of infinitesimal multi-parameter…