Topic
Toric variety
About: Toric variety is a research topic. Over the lifetime, 2630 publications have been published within this topic receiving 65604 citations. The topic is also known as: torus embedding.
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01 Jan 1998
TL;DR: In this paper, a detailed analysis of the GKZ (Gel'fand, Kapranov and Zelevinski) hypergeometric systems in the context of mirror symmetry of Calabi-Yau hypersurfaces in toric varieties is presented.
Abstract: We present a detailed analysis of the GKZ (Gel’fand, Kapranov and Zelevinski) hypergeometric systems in the context of mirror symmetry of Calabi-Yau hypersurfaces in toric varieties. As an application, we will derive a concise formula for the prepotential about large complex structure limits.
20 citations
Dissertation•
01 Jan 2000
TL;DR: The authors estudian singularidades casi-ordinarias de variedades analiticas complejas, por medio de tecnicas de la geometria torica, principalmente en el caso de germenes de hipersuperficies.
Abstract: Se estudian las singularidades casi-ordinarias de variedades analiticas complejas, por medio de tecnicas de la geometria torica, principalmente en el caso de germenes de hipersuperficies.
20 citations
TL;DR: The primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.
Abstract: We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the $A$-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.
20 citations
TL;DR: In this article, the vector space T 1 of first-order infinitesimal deformations for affine toric varieties X σ was computed using combinatorial data of the given cone σ only.
20 citations
TL;DR: In this article, it was shown that for a compact toric manifold whose anti-canonical divisor is numerically effective, the Lagrangian Floer superpotential defined by Fukaya-Oh-Ohto-Ono is equal to that defined by using the toric mirror map under a convergence assumption.
Abstract: We prove that for a compact toric manifold whose anti-canonical divisor is numerically effective, the Lagrangian Floer superpotential defined by Fukaya-Oh-Ohto-Ono is equal to the superpotential written down by using the toric mirror map under a convergence assumption. This gives a method to compute open Gromov-Witten invariants using mirror symmetry.
20 citations