Projective toric varieties are described either by lattice polytopes in the character group of the torus, or by a polyhedral fan. In the latter case, the projective embedding is encoded by a piecewise linear function on the fan. We will generalize this concept to the case of torus actions of smaller dimension such as the action of (C) on Grass(2, n). The resulting description includes a direct ...

The recent discovery that there is a tight polyhedral immersion of the projective plane with one handle, while there is no smooth tight immersion of the same surface, provides a rare example in low dimensions of a significant difference between smooth and polyhedral surfaces. In this paper the author shows that the obstruction to smoothing the polyhedral model is not local in nature, and descri...

Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.

In undergoing this life, many people always try to do and get the best. New knowledge, experience, lesson, and everything that can improve the life will be done. However, many people sometimes feel confused to get those things. Feeling the limited of experience and sources to be better is one of the lacks to own. However, there is a very simple thing that can be done. This is what your teacher ...

We propose a method to model and control topological changes by a smooth deformation of a polyhedral mesh using curves and loops. As changing the genus of a surface is not a continuous transformation, the topological change is made when an intermediate shape between the two topologies has been obtained. The creation and the deletion of holes are studied. The deletion of a hole uses non nullhomo...

We construct a polyhedron that is topologically convex (i.e., has the graph of a convex polyhedron) yet has no vertex unfolding: no matter how we cut along the edges and keep faces attached at vertices to form a connected (hinged) surface, the surface necessarily unfolds with overlap.

Classical polyhedral representations of imperative languages entangle untranslated scalar imperative operations to the declarative descriptions of the polyhedral model. This representation can handle high level array operations, but is more difficult to work on programs that split the array computations in smaller chunks involving scalar temporary variables. The aim of the current paper is to p...

We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in R. We also provide examples of minimal vertex triangulations of closed, connected, orientable 2-manifolds of genus 5 that do not admit any polyhedral embeddings. We construct a new infinite family of non-realizable triangulations of surfaces. These results were ...

The following generalization of the Hopf conjecture is proved: if the fundamental group of an n-dimensional compact polyhedral space M without boundary and with no conjugate points has polynomial growth, then there exists a finite covering of M by a flat torus. §