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

This is the paper as published. The topology of a complex plane curve singularity with real branches is deduced from any real deformation having delta crossings. An example of the computation of the global geometric monodromy of a…

We show the existence of toric resolution tower for an irreducible curve singularity which is explicitly described by Tschirnhausen polynomials. We deduce for a smooth affine plane curve from its topology restrictions for its singularity at…

We show that every graph admits a canonical tree-like decomposition into its $k$-edge-connected pieces for all $k\in\mathbb{N}\cup\{\infty\}$ simultaneously.

We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as…

We consider plane curves isomorphic to C*. We prove that with one exception the branches at infinity can be separated by an automorphism of C^2. We also give a bound for selfintersection number of the resolution curve.

We prove that small deformations of canonical singularities are canonical.

In the article, we exhibit a series of new examples of rigid plane curves, that is, curves, whose collection of singularities determines them almost uniquely up to a projective transformation of the plane.

On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. The corresponding deformation can be viewed as a quantization, in which the broken line…

We prove that there exists an algorithm for determining whether two piecewise-linear spatial graphs are isomorphic. In its most general form, our theorem applies to spatial graphs furnished with vertex colorings, edge colorings and/or edge…

We study the pull-back of regular 1-forms on a complex irreducible plane curve singularity under the normalization morphism.

The dual complex associated to a resolution of singularities generalizes the notion of a resolution graph of a surface singularity to any dimension. We show that homotopy type of the dual complex is an invariant of an isolated singularity.

Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real roots of a univariate polynomial that can be derived from…

We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.

We find a geometrical method of analysing the singularities of a plane nodal curve. The main results will be used in a forthcoming paper on geometric Plucker formulas for such curves. Plane nodal curves, that is plane curves having at most…

We classify the possible ramification data and etale local structure of orders over surfaces with canonical singularities.

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite…

The decomposition group of an irreducible plane curve $X\subset\mathbb P^2$ is the subgroup $\mathrm{Dec}(X)\subset\mathrm{Bir}(\mathbb P^2)$ of birational maps which restrict to a birational map of $X$. We show that $\mathrm{Dec}(X)$ is…

We describe the embedded resolution of a quasi-ordinary surface singularity (V,p) which results from applying the canonical resolution of Bierstone-Milman to (V,p). We show that this process depends solely on the characteristic pairs of…

We look at the decomposition of the compactified jacobian of a singular curve into components and discuss some examples.

This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…