We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gröbner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gröbner basis. This was proved by Eisenbud–Reeves–Totaro in the case where coordinates are generic. Our proof doe...

Let us first recall our setting. In the toric case, there is a correspondence between n-dimensional nonsingular Fano varieties and ndimensional Fano polytopes, where the Fano varieties are biregular isomorphic if and only if the corresponding Fano polytopes are unimodularly equivalent. Here, given a lattice N of rank n, a Fano polytope Q ⊆ NR := N ⊗Z R is given as a lattice polytope containing ...

From tomorrow onwards, we will be working with toric stacks, but today we’ll be more general. Let f : Γ → X be a stable representable morphism from an orbi-curve to a stack. An orbi-curve is a proper, projective, algebraic curve Γ with some marked points xi. Each of the marked points has a chart of the form [∆/μri ] (where ∆ is a disk and μr is the group of r-th roots of unity). An orbi-curve h...

Anterior segment fluorophotometry (topical) and central endothelial cell photography were performed on 40 long-term (2-23 years) contact lens wearers (four groups of ten each: hard, soft, gas permeable, and gas permeable plus prior lens usage) and 40 non-contact lens wearers of similar ages. Morphologically, the endothelial cells of contact lens wearers showed greater variability in size and sh...

Lens flexure and residual astigmatism were evaluated with rigid gas permeable (RGP) contact lenses made in low, medium, and high oxygen permeable (Dk) materials to determine if significant differences would be apparent as lens Dk was changed. Fourteen successful RGP contact lens wearers had their customary lens parameters, including lens thickness, held constant in duplicate pairs made in low (...

PURPOSE To describe the epidemiology of children submitted to contact lens fit. METHODS Retrospective study of 73 children that had been submitted to contact lens fit at the "Universidade Federal de São Paulo". This study analyzed sex distribution, age, diagnosis, indications and contact lens fitted at first examination. RESULTS 34 children (46.6%) were male and 39 (53.4%) female, aged betw...

We first construct a derived equivalence between a small crepant resolution of an affine toric Calabi-Yau 3-fold and a certain quiver with a superpotential. Under this derived equivalence we establish a wallcrossing formula for the generating function of the counting invariants of perverse coherent sheaves. As an application we provide some equations on Donaldson-Thomas, Pandeharipande-Thomas a...