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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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109 citations
TL;DR: In this paper, the authors constructed an A∞ category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of a smooth projective toric variety X, which is quasi-equivalent to the DG category of line bundles on X.
Abstract: Given a smooth projective toric variety X, we construct an A∞ category of Lagrangians with boundary on a level set of the Landau–Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line bundles on X.
108 citations
106 citations
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TL;DR: In this article, the authors define basic concepts of complex and Kahler geometry, and then proceed with an analysis of various definitions of Calabi-Yau manifolds, and provide a short introduction to toric geometry, aimed at constructing CYF in two different ways: as hypersurfaces in toric varieties and as local toric CalabiYau threefolds.
Abstract: These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi-Yau manifolds in two different ways: as hypersurfaces in toric varieties and as local toric Calabi-Yau threefolds. These lecture notes supplement a mini-course that was given by the author at the Modave Summer School in Mathematical Physics 2005, and at CERN in 2007.
106 citations
TL;DR: In this article, the notion of a reflexive polytope which appeared in connection to mirror symmetry was introduced and generalized to non-ingular toric Fano varieties, and new classification results, bounds of invariants and conjectures concerning combinatorial and geometrical properties of reflexive Polytopes were derived.
Abstract: 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 generalizations 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 combinatorial and geometrical properties of reflexive polytopes.
106 citations