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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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34 citations
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TL;DR: The construction and several techniques for estimating the minimum distance are described first and connections with the theories of toric codes and order domains are briefly indicated.
Abstract: This paper is a general survey of literature on Goppa-type codes from higher dimensional algebraic varieties. The construction and several techniques for estimating the minimum distance are described first. Codes from various classes of varieties, including Hermitian hypersurfaces, Grassmannians, flag varieties, ruled surfaces over curves, and Deligne-Lusztig varieties are considered. Connections with the theories of toric codes and order domains are also briefly indicated.
34 citations
TL;DR: Mirror symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed in this article for Calabi-Yau spaces with two and three moduli.
Abstract: Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.
34 citations
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TL;DR: In this article, the authors present an upper bound on the number of possible fake weighted projective spaces with only terminal (or canonical) singularities for a fixed dimension, assuming that the singularities of the projective space have only terminal singularities.
Abstract: A fake weighted projective space X is a Q-factorial toric variety with Picard number one. As with weighted projective space, X comes equipped with a set of weights (\lambda_0,...,\lambda_n). We see how the singularities of P(\lambda_0,...,\lambda_n) influence the singularities of X, and how the weights bound the number of possible fake weighted projective spaces for a fixed dimension. Finally, we present an upper bound on the ratios \lambda_j/\sum\lambda_i if we wish X to have only terminal (or canonical) singularities.
34 citations
TL;DR: In this paper, the authors give a method for computing the syzygies of the coordinate ring R of an affine toric variety, which works for dimension one and two cases, Cohen-Macaulay semigroups, and for computing minimal generators of the defining ideal.
34 citations