We show that the pseudoeffective cone of divisors $\overline{\text{Eff}}^1(\overline{\mathcal{M}}_{g,n})$ for $g\geq 2$ and $n\geq is not polyhedral by showing class fibre morphism forgetting one point forms an extremal ray dual nef curves $\overline{\text{Nef}}_1(\overline{\mathcal{M}}_{g,n})$ at this polyhedral.

Abstract We present a generalization of the notion neighborliness to non-polyhedral convex cones. Although definition is available in case literature, it fairly restrictive as requires all low-dimensional faces be polyhedral. Our approach more flexible and includes, for example, cone positive-semidefinite matrices special (this not neighborly general). term our Terracini convexity due its conce...

We seek to extend the scope and efficiency of iterative compilation techniques by searching not only for program transformation parameters but for the most appropriate transformations themselves. For that purpose, we need to find a generic way to express program transformations and compositions of transformations. In this article, we introduce a framework for the polyhedral representation of a ...

We propose a method to approximate a polyhedral object with a deformable smooth surface, namely the t-skin defined by Edelsbrunner for all 0 < t < 1. We guarantee that they are homeomorphic and their Hausdorff distance is at most ε > 0. This construction makes it possible for fully automatic, smooth and robust deformation between two polyhedral objects with different topologies. En route to our...

This work concerns the approximation of the shape operator of smooth surfaces in R from polyhedral surfaces. We introduce two generalized shape operators that are vector-valued linear functionals on a Sobolev space of vector fields and can be rigorously defined on smooth and on polyhedral surfaces. We consider polyhedral surfaces that approximate smooth surfaces and prove two types of approxima...

Constraining 3D meshes to restricted classes is necessary in architectural and industrial design, but it can be very challenging to manipulate meshes while staying within these classes. Specifically, polyhedral meshes those having planar faces are very important, but also notoriously difficult to generate and manipulate efficiently. We describe an interactive method for computing, optimizing an...

We investigate the rigidity of hyperbolic cone metrics on 3-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyperideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is d...

I present a novel framework for polyhedral mesh editing with face-based projective maps, that preserves planarity by definition. Such meshes are essential in the fields of construction and architectural design. By using homogeneous coordinates to describe vertices, we gain a rich and linear shape space of meshes with planar faces. The generality of this space allows for polyhedral geometric pro...

Let Σ be a surface. We prove that rigidity indices of graphs which admit a polyhedral embedding in Σ and 5-connected graphs admitting an embedding in Σ are bounded by a constant depending on Σ. Moreover if the Euler characteristic of Σ is negative, then the separation index of graphs admitting a polyhedral embedding in Σ is also bounded. As a side result we show that distinguishing number of bo...