Related papers: Endomorphisms of the plane preserving a pencil of …
We associate each endomorphism of a finite cyclic group with a digraph and study many properties of this digraph, including its adjacent matrix and automorphism group.
We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
The order in which plane-filling curves visit points in the plane can be exploited to design efficient algorithms. Typically, the curves are useful because they preserve locality: points that are close to each other along the curve tend to…
Many classes of maps are characterized as (possibly multi-valued) maps preserving particular types of compact filters.
We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies.
Any knot group is the image of the group of a prime knot by a homomorphism that preserves peripheral structure. In fact, there are infinitely many such prime knots. A related partial order on knots is defined, and its properties are…
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
We study the pull-back of regular 1-forms on a complex irreducible plane curve singularity under the normalization morphism.
We study the stability of pencils of plane sextics in the sense of geometric invariant theory. In particular, we obtain a complete and geometric description of the stability of Halphen pencils of index two.
We construct the infinite sequence of invariants for curves in surfaces by using word theory that V. Turaev introduced. For plane closed curves, we add some extra terms, e.g. the rotation number. From these modified invariants, we get the…
In this paper we investigate the relationships between envelopes of circle families and some special curves in the plane, such as evolutes, pedals, evolutoids and pedaloids.
We classify the endomorphism algebras of factors of the Jacobian of certain hypergeometric curves over a field of characteristic zero. Other than a few exceptional cases, the endomorphism algebras turn out to be either a cyclotomic field…
In this paper, we consider a new length preserving curve flow for convex curves in the plane. We show that the global flow exists, the area of the region bounded by the evolving curve is increasing, and the evolving curve converges to the…
We introduce the notion of microlocal versal deformation of a plane curve. We construct equisingular versal deformations of Legendrian curves that are the conormal of a semi-quasi-homogeneous branch.
We construct a good compactification of the variety of irreducible projective plane curves of degree n with d nodes and no other singularities.
Given two irreducible curves of the plane which have isomorphic complements, it is natural to ask whether there exists an automorphism of the plane that sends one curve on the other. This question has a positive answer for a large family of…
We study the algebraic dynamics of endomorphisms of projective varieties. First, we characterize their iterated images, i.e. the intersection of the images of their iterates. Next, we explore the Stein factorizations of the iterates,…
In this article, we describe all the group morphisms from the group of orientation-preserving homeomorphisms of the circle to the group of homeomorphisms of the annulus or of the torus.