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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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TL;DR: In this paper, it was shown that the automorphism group of a complete toric Fano variety is reductive if the barycenter of the associated reflexive polytope is zero.
Abstract: We give equivalent and sufficient criteria for the automorphism group of a complete toric variety, respectively a Gorenstein toric Fano variety, to be reductive. In particular we show that the automorphism group of a Gorenstein toric Fano variety is reductive, if the barycenter of the associated reflexive polytope is zero. Furthermore a sharp bound on the dimension of the reductive automorphism group of a complete toric variety is proven by studying the set of Demazure roots.
46 citations
TL;DR: In this paper, the authors considered an orbifold X obtained by a Kahler reduction of C n, and defined its hyperkahler analogue M as a hyper-ahler reduction T*C n ≅ H n by the same group.
Abstract: We consider an orbifold X obtained by a Kahler reduction of C n , and we define its hyperkahler analogue M as a hyperkahler reduction of T*C n ≅ H n by the same group. In the case where the group is abelian and X is a toric variety, M is a toric hyperkahler orbifold, as defined in Bielawski and Dancer, 2000, and further studied by Konno and by Hausel and Sturmfels. The variety M carries a natural action of S 1 , induced by the scalar action of S 1 on the fibers of T*C n . In this paper we study this action, computing its fixed points and its equivariant cohomology. As an application, we use the associated Z 2 action on the real locus of M to compute a deformation of the Orlik-Solomon algebra of a smooth, real hyperplane arrangement H, depending nontrivially on the affine structure of the arrangement. This deformation is given by the Z 2 -equivariant cohomology of the complement of the complexification of H, where Z 2 acts by complex conjugation.
46 citations
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TL;DR: In this article, the moduli space of quiver representations associated with a dimer model was shown to be smooth for a general stability parameter, and it was shown that the modulus space in this case is a crepant resolution of the toric variety determined by the Newton polygon of the characteristic polynomial.
Abstract: We give a sufficient condition for the moduli space of quiver representations associated with a dimer model to be smooth for a general stability parameter. We also show that the moduli space in this case is a crepant resolution of the toric variety determined by the Newton polygon of the characteristic polynomial.
46 citations
TL;DR: In this paper, the following result is proved: given smooth toric 3-folds and and a proper birational toric morphism, the morphism decomposes as a composite of blow-ups and blow-downs in the toric strata.
Abstract: The following result is proved. Suppose given smooth toric 3-folds and and a proper birational toric morphism . Then decomposes as a composite of blow-ups and blow-downs in smooth toric strata. Bibliography: 7 titles.
45 citations
TL;DR: The notion of a k-convex support function for a toric variety is introduced in this paper, and a criterion for a line bundle L to generate k-jets on X is given in terms of the k-Convexity of the support function, and L is proved to be k-jet ample if and only if each invariant curve has degree at least k.
Abstract: The notion of a k-convex \(\Delta\)-support function for a toric variety \(X(\Delta)\) is introduced A criterion for a line bundle L to generate k-jets on X is given in terms of the k-convexity of the \(\Delta\)-support function \(\psi_L\) Equivalently L is proved to be k-jet ample if and only if the restriction to each invariant curve has degree at least k
45 citations