2 Background in toric geometry 8 2.1 Basic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Toric varieties associated with a reflexive polyhedron . . . . . . . 10 2.3 Subtoric varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Singularities of a simplicial toric variety . . . . . . . . . . . . . . 12 2.5 Toric action of a torus on a toric variety . ...

In [GrSi2] we gave a canonical construction of degenerating families of varieties with effective anticanonical bundle. The central fibre X of such a degeneration is a union of toric varieties, glued pairwise torically along toric prime divisors. In particular, the notion of toric strata makes sense on the central fiber. A somewhat complementary feature of our degeneration is their toroidal natu...

purpose : the objective of this study was to evaluate the outcome of acrysof toric intraocular lenses (iols) implantation in cataract surgery for the correction of regular corneal astigmatism. methods : twenty eyes of 16 patients with cataract and regular corneal astigmatism of 1.00-4.00 diopter (d) underwent surgery. depending on the amount of corneal astigmatism, an acrysof toric iol of type ...

A toric integrable geodesic flow on a manifold M is a completely integrable geodesic flow such that the integrals generate a homogeneous torus action on the punctured cotangent bundle T ∗M \ M . A toric integrable manifold is a manifold which has a toric integrable geodesic flow. Toric integrable manifolds can be characterized as those whose cosphere bundle (the sphere bundle in the cotangent b...

We study residues on a complete toric variety X , which are defined in terms of the homogeneous coordinate ring of X . We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on ...

Generalizing toric varieties, we introduce toric Deligne-Mumford stacks. The main result in this paper is an explicit calculation of the orbifold Chow ring of a toric Deligne-Mumford stack. As an application, we prove that the orbifold Chow ring of the toric Deligne-Mumford stack associated to a simplicial toric variety is a flat deformation of (but is not necessarily isomorphic to) the Chow ri...

We associate to each toric vector bundle on a toric variety X(∆) a “branched cover” of the fan ∆ together with a piecewise-linear function on the branched cover. This construction generalizes the usual correspondence between toric Cartier divisors and piecewise-linear functions. We apply this combinatorial geometric technique to study the moduli of toric vector bundles with fixed equivariant Ch...

PURPOSE To present a case of traumatic dislocation of an Ophtec Artisan phakic intraocular lens (PIOL) and an analysis of the endothelial cell count. METHODS The patient presented with blurred vision in his left eye after sustaining a brow laceration. History included uncomplicated bilateral implantation of an Artisan PIOL to correct myopia. RESULTS The brow laceration was sutured and topic...

Generalizing toric varieties, we introduce toric Deligne-Mumford stacks which correspond to combinatorial data. The main result in this paper is an explicit calculation of the orbifold Chow ring of a toric Deligne-Mumford stack. As an application, we prove that the orbifold Chow ring of the toric Deligne-Mumford stack associated to a simplicial toric variety is a flat deformation of (but is not...

We prove a formula for the orbifold Chow ring of semi-projective toric DM stacks, generalizing the orbifold Chow ring formula of projective toric DM stacks by BorisovChen-Smith. We also consider a special kind of semi-projective toric DM stacks, the Lawrence toric DM stacks. We prove that the orbifold Chow ring of a Lawrence toric DM stack is isomorphic to the orbifold Chow ring of its associat...