We introduce a notion of balanced configurations of vectors. This is motivated by the study of rational A-hypergeometric functions in the sense of Gelfand, Kapranov and Zelevinsky. We classify balanced configurations of seven plane vectors up to GL(2,R)-equivalence and deduce that the only gkz-rational toric four-folds in P6 are those varieties associated with an essential Cayley configuration....

In [Kat94b], Kato defined his notion of a log regular scheme and studied the local behavior of such schemes. A toric variety equipped with its canonical logarithmic structure is log regular. And, these schemes allow one to generalize toric geometry to a theory that does not require a base field. This paper will extend this theory by removing normality requirements.

We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for nonsingular toric Fano varieties. As applications we obtain new classification results, bounds of invariants and formulate conjectures concerning combinatoria...

We prove the following results for toric Deligne–Mumford stacks, under minimal compactness hypotheses: the Localization Theorem in equivariant K-theory; the equivariant Hirzebruch–Riemann–Roch theorem; the Fourier–Mukai transformation associated to a crepant toric wall-crossing gives an equivariant derived equivalence.

PURPOSE To compare visual outcomes and performance between bilateral implantation of a diffractive trifocal intraocular lens (IOL) Acrysof®PanOptix® TFNT00 and blended implantation of two different near add power bifocal IOLs: Acrysof® Restor® SV25T0 in dominant eye and Acrysof® Restor® SN6AD1 in the nondominant eye. METHODS This prospective, nonrandomized, consecutive and comparative study a...

Let O be a symplectic toric orbifold with a fixed T-action and with a toric Kähler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace operator ∆g on C∞(O) determines the moment polytope of O, and hence by Delzant’s theorem determines O up to symplectomorphism. In the setting of toric orbifolds we significantly improve upon our previous results a...

Dropping separatedness in the definition of a toric variety, one obtains the more general notion of a toric prevariety. Toric prevarieties occur as ambient spaces in algebraic geometry and moreover they appear naturally as intermediate steps in quotient constructions. We first provide a complete description of the category of toric prevarieties in terms of convex–geometrical data, so–called sys...

Lens damage during phakic intraocular lens implantation is a major complication. A case of a patient who developed lens vacuoles during toric implantable collamer lens (ICL) removal from her right eye and insertion of a new non-toric ICL due to persistent rotation of the former is presented in this work. As this event is very uncommon when implanting phakic intraocular lenses, the performed sur...

BACKGROUND With increasing availability of toric intraocular lenses (IOL) for cataract surgery, real-world refractive outcome data is needed to aid the counselling of patients regarding lens choice. We aim to assess the outcomes of toric intraocular lens use in the non-specialist environment of a typical United Kingdom NHS cataract service. METHODS A retrospective cohort study conducted at th...

PURPOSE To compare the rates of lens epithelial cell (LEC) migration and posterior capsule opacification (PCO) 1 and 3 years after sutureless small incision phacoemulsification and in-the-bag implantation of 2 acrylic polymer intraocular lenses (IOLs)-the AcrySof and MemoryLens-in fellow eyes of patients. SETTING Eye Clinic, Beyoğlu Education and Research Hospital, Istanbul, Turkey. METHODS...