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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TL;DR: In this article, the authors generalize this classification to normal toric varieties over an arbitrary valuation ring of rank one, based on a generalization of Sumihiro's theorem to this non-noetherian setting.
Abstract: Normal toric varieties over a field or a discrete valuation ring are classified by rational polyhedral fans. We generalize this classification to normal toric varieties over an arbitrary valuation ring of rank one. The proof is based on a generalization of Sumihiro’s theorem to this non-noetherian setting. These toric varieties play an important role for tropicalizations. MSC2010: 14M25, 14L30, 13F30
17 citations
TL;DR: The first application of the open mirror symmetry to the compact non-complete intersections in toric variety is presented in this article, where the number of disk invariants of some examples is predicted by using the direct integration method proposed recently.
Abstract: We investigate the open mirror symmetry of certain non-complete intersection Calabi-Yau 3-folds, called pfaffian Calabi-Yau. We predict the number of disk invariants of some examples by using the direct integration method proposed recently and the open mirror symmetry. We treat several pfaffian Calabi-Yau 3-folds and branes with two discrete vacua. Some models have two special points in its moduli space, around both of which we can consider different A-model mirror partners. We compute disc invariants for both cases. This study is the first application of the open mirror symmetry to the compact non-complete intersections in toric variety.
17 citations
TL;DR: In this paper, a new method for determining the complete set of dynamically balanced planar four-bar mechanisms is presented using complex variables to model the kinematics of the mechanism, the static and dynamic balancing constraints are written as algebraic equations over complex variables and joint angular velocities after elimination of the joint angular velocity variables, the problem is formulated as a problem of factorization of Laurent polynomials.
17 citations
TL;DR: For an algebraic curve that has only simplest singularities and only rational irreducible components, the generalized Jacobian coincides with the moduli variety of topologically trivial linear bundles whose canonical compactification is a toric variety constructed from a convex integer polytope as discussed by the authors.
Abstract: For an algebraic curve that has only simplest singularities and only rational irreducible components, the generalized Jacobian coincides with the moduli variety of topologically trivial linear bundles whose canonical compactification is a toric variety constructed from a convex integer polytope. The vertices of this polytope are the simple cycles in the one-dimensional rational homology space of the dual graph of this curve. It is proved that for three-connected graphs the simple cycle polytope uniquely determines the graph.
17 citations
17 citations