Related papers: The movable cone via intersections
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
We give a geometric construction of tilting perverse sheaves using stratified Morse theory, torus actions, and nearby cycles.
We introduce a new approach to build microscopic engines on the atomic scale that move translationally or rotationally and can perform useful functions such as pulling of a cargo. Characteristic of these engines is the possibility to…
In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…
A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t). In this paper, we investigate when parameter curves of the canal surface are also…
Let X be a (possibly nodal) K-trivial threefold moving in a fixed ambient space P. Suppose X contains a continuous family of curves, all of whose members satisfy certain unobstructedness conditions in P. A formula is given for computing the…
Dynamics of rough discs in a rarified media is considered. We study possible trajectories of centers of discs. The main result of the paper is the following: any finite rectifiable curve can be approximated by trajectories of centers of…
We describe a construction (the `warped cone construction') which produces examples of coarse spaces with large groups of translations. We show that by this construction we can obtain many examples of coarse spaces which do not have…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
We determine the crossing number of polynomial size curve systems on standard surfaces, in terms of the genus, up to high precision.
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
The complex interactions of localized vortices with waves is investigated using a model of point vortices in the presence of a transverse or longitudinal wave. This simple model shows a rich dynamical behavior including oscillations of a…
The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor…
We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape…
In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and its global section. We also study…
We characterise when a set of simple closed curves in an orientable surface forms a bouquet, in terms of relations between the corresponding Dehn twists.
For affine algebraic plane curves we reduce a calculation of its invariants to calculation of the intersection of kernels of some derivations.
Let G be an arbitrary simple graph. The main results are explicit representations of the edge cone of G as a finite intersection of closed halfspaces. If G is bipartite and connected we determine the facets of the edge cone and present a…
We describe a close relation between wall crossings in the birational geometry of moduli space of Gieseker stable sheaves $M_H(v)$ on $\bb{P}^2$ and mini-wall crossings in the stability manifold $Stab(D^b(\bb{P}^2))$.