Related papers: Three-dimensional terminal toric flips
We factorize three-dimensional terminal flops into a composition of divisorial contractions to points and blowing-up smooth curves.
We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds…
This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…
We survey some results on toric topology.
Determining the associated metrics we get a local classification of contact metric three manifolds.
We show that 3-fold terminal flips and divisorial contractions may be factored into a sequence of flops, blow-downs to a smooth curve in a smooth 3-fold or divisorial contractions to points with minimal discrepancies.
We discuss how triposes may be understood as generalizations of localic geometric morphisms.
We define and examine flip operations for quadrilateral and hexahedral meshes, similar to the flipping transformations previously used in triangular and tetrahedral mesh generation.
We give a brief survey of abelian torsions of 3-manifolds.
We completely classify the Q-factorial terminal toric Fano three-folds such that the sum of the squared torus invariant prime divisors is non-negative.
We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint locally geodesic segments. We prove that the flip graph of geometric triangulations with fixed vertices of a flat torus or a…
The paper explores the birational geometry of terminal quartic 3-folds. In doing this I develop a new approach to study maximal singularities with positive dimensional centers. This allows to determine the pliability of a Q-factorial…
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…
The goal of this article is to survey recent developments in the theory of contact structures in dimension three.
The dynamics of a nanoelectromechanical system in the form of a three-terminal tunneling device is studied by analytical and numerical methods. The main results are the existence of bistable stationary states resulting in directly…
We consider domino tilings of three-dimensional cubiculated manifolds with or without boundary, including subsets of Euclidean space and three-dimensional tori. In particular, we are interested in the connected components of the space of…
In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.
We prove that for a given flat surface with conical singularities, any pair of geometric triangulations can be connected by a chain of flips.
We present an improved version of the cyclic covering trick, which works inside the category of toroidal embeddings