Related papers: Positive neighborhoods of curves

We study neighborhoods of rational curves in surfaces with self-intersection number 1 that can be linearised.

We bound the genus of a projective curve lying on a complete intersection surface in terms of its degree and the degrees of the defining equations of the surface on which it lies.

We investigate complex analytic properties of a neighborhood of a reduced rational curve with an ordinary cusp embedded in a non-singular complex surface whose self-intersection number is zero.

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…

In this paper we study degree three curves in $C^{(2)}$ with positive self-intersection defined by the action of a spherical triangular group in an auxiliary curve.

We introduce an operation that measures the self intersections of paths on a surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson…

We determine the convergence regions of certain local integrals on the moduli spaces of curves in neighborhoods of fixed stable curves in terms of the combinatorics of the corresponding graphs.

The embeddings of complex plane projective curves in the plane are a cornerstone of the topological study of algebraic varieties. In this work, we deal with the local and global aspects of these embeddings, with a special attention to its…

We describe each multiple curve on the orientable surface of genus-$g$ with $n$ punctures and one boundary component by using this multiple curve's geometric intersection number with the embedded curves in this surface.

We study curves consisting of unions of projective lines whose intersections are given by graphs. Under suitable hypotheses on the graph, these so-called \emph{graph curves} can be embedded in projective space as line arrangements. We…

We investigate the geometry of smooth hyperelliptic curves that possess additional involutions, especially from the point of view of the Prym theory. Our main result is the injectivity of the Prym map for hyperelliptic…

A surface embedded in space, in such a way that each point has a neighborhood within which the surface is a terrain, projects to an immersed surface in the plane, the boundary of which is a self-intersecting curve. Under what circumstances…

We derive spectral sequences for the intersection homology of stratified fibrations and approximate tubular neighborhoods in manifold stratified spaces. These neighborhoods include regular neighborhoods in PL stratified spaces.

We give an explicit formula for the self-intersection number of negative curves on Fermat surfaces. The formula offers us hints to either prove or disprove the Bounded Negativity Conjecture for the Fermat surfaces.

Let X be a smooth projective curve over a perfect field k of positive characteristic. This work investigates the relationship between stratified cohomology and group cohomology of the stratified fundamental group of X.

Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the…

We consider the relations between different measures of complexity for free homotopy classes of curves on a surface $\Sigma$, including the minimum number of self-intersections, the minimum length of the words representing them in a…

We apply contact homology to obtain new results in the problem of distinguishing immersed plane curves without dangerous self-tangencies.

On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…

We prove the existence of embedded closed constant curvature curves on convex surfaces.