相关论文: On the Resolution Graph of a Plane Curve

We study families of plane algebraic curves sharing the same set of foci. We reformulate confocality via a focal map on equiclassical families and analyze its fibers using deformation theory.

The Hessian Topology is a subject having interesting relations with several areas, for instance, differential geometry, implicit differential equations, analysis and singularity theory. In this article we study the problem of realization of…

This short note provides a quick introduction to relative canonical resolutions of curves on rational normal scrolls. We present our Macaulay2-package which computes the relative canonical resolution associated to a curve and a pencil of…

We study the classification of plane curve singularities in arbitrary characteristic. We first give a bound for the determinacy of a plane curve singularity with respect to pararametrization equivalence in terms of its conductor. Then we…

We prove that the topological recursion formalism can be used to quantize any generic classical spectral curve with smooth ramification points and simply ramified away from poles. For this purpose, we build both the associated quantum…

In this paper we solve the problem of analytic classification of plane curves singularities with two branches by presenting their normal forms. This is accomplished by means of a new analytic invariant that relates vectors in the tangent…

A new generalization of the classical separate algebraicity theorem is suggested and proved.

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

We prove that, if two germs of plane curves $(C,0)$ and $(C',0)$ with at least one singular branch are equivalent by a (real) smooth diffeomorphism, then $C$ is complex isomorphic to $C'$ or to $\overline{C'}$. A similar result was shown by…

Rational algebraic curves have been intensively studied in the last decades, both from the theoretical and applied point of view. In applications (e.g. level curves, linear homotopy deformation, geometric constructions in computer aided…

Every finite graph $G$ can be decomposed in a canonical way that displays its local connectivity-structure [DJKK26]. These decompositions are defined via a suitable more tree-like covering of $G$, whose tangle-tree structure is projected…

In this paper, we consider deformations of singular complex curves on complex surfaces. Despite the fundamental nature of the problem, little seems to be known for curves on general surfaces. Let $C\subset S$ be a complete integral curve on…

We consider uniformly resolvable decompositions of $K_v$ into subgraphs such that each resolution class contains only blocks isomorphic to the same graph. We give a partial solution for the case in which all resolution classes are either…

For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane closed curve whose chord diagram contains the given chord diagram as a…

We prove autoduality for curves of compact type and, more generally, treelike curves with planar singularities. More precisely, we produce an isomorphism between the generalized Jacobian of such a curve and the connected component of the…

We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.

In this paper we consider the uniformly resolvable decompositions of the complete graph $2K_v$ into subgraphs where each resolution class contains only blocks isomorphic to the same graph. We completely determine the spectrum for the cases…

We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.

We show that a sequence of smooth analytic curves of the unit ball of the complex plane, for which the genus is bounded by the area, converges to a lamination in a weak sense.

We describe degenerations of projective plane curves to curves containing a fixed line $l$ as a component, and show that $H^1({\overline V}_{n,d,m}, {\Cal O} (r))=0, r \in{\Bbb Z}$, where $V_{n,d,m}\subset {\Bbb P}^N (N = n(n+3)/2)$ is the…