Open AccessJournal Article
Review: Tadao Oda, Convex bodies and algebraic geometry: An introduction to toric varieties
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This article is published in Bulletin of the American Mathematical Society.The article was published on 1989-10-01 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Function field of an algebraic variety & Real algebraic geometry.read more
Citations
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Quantum cohomology of smooth complete intersections in weighted projective spaces and in singular toric varieties
TL;DR: In this article, Gromov-Witten invariants for Fano varieties of dimension ≥ 3 that are complete intersections in weighted projective spaces or singular toric varieties were obtained.
Journal ArticleDOI
Additive actions on toric varieties
TL;DR: In this article, it was shown that if a complete toric variety admits an additive action normalized by the acting torus, then it admits a complete collection of Demazure roots of the fan of the variety.
Posted Content
On uniqueness of additive actions on complete toric varieties
TL;DR: In this paper, a uniqueness criterion for additive action on a complete toric variety is given, where the uniqueness criterion requires that the additive action is a regular effective action with an open orbit of the commutative unipotent group.
Posted Content
Blowups in tame monomial ideals
Eleonore Faber,Dennis B. Westra +1 more
TL;DR: In this paper, the authors study blowups of affine n-space with center an arbitrary monomial ideal, and give a combinatorial criterion to decide whether the blowup is smooth and apply this criterion to discuss a smoothing procedure proposed by Rosenberg, monomial building sets and permutohedra.
Journal ArticleDOI
Gale duality and homogeneous toric varieties
TL;DR: In this paper, it was shown that a non-degenerate toric variety X is called S-homogeneous if the subgroup of the automorphism group Aut(X) generated by root subgroups acts on X transitively.
References
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Journal ArticleDOI
Additive actions on toric varieties
TL;DR: In this article, it was shown that if a complete toric variety admits an additive action normalized by the acting torus, then it admits a complete collection of Demazure roots of the fan of the variety.
Posted Content
On uniqueness of additive actions on complete toric varieties
TL;DR: In this paper, a uniqueness criterion for additive action on a complete toric variety is given, where the uniqueness criterion requires that the additive action is a regular effective action with an open orbit of the commutative unipotent group.
Journal ArticleDOI
Blowups in tame monomial ideals
Eleonore Faber,Dennis B. Westra +1 more
TL;DR: Tame monomial ideals as discussed by the authors are a class of ideals that render smooth blowups of affine n -space, and they have been used in many applications, such as a smoothing procedure proposed by Rosenberg, building sets and permutohedra.
Journal ArticleDOI
Gale duality and homogeneous toric varieties
TL;DR: In this paper, it was shown that a non-degenerate toric variety X is called S-homogeneous if the subgroup of the automorphism group Aut(X) generated by root subgroups acts on X transitively.
Posted Content
Quantum cohomology of smooth complete intersections in weighted projective spaces and singular toric varieties
TL;DR: This paper generalized Givental's theorem for complete intersections in smooth toric varieties in the Fano case and derived Gromov-Witten invariants of Fano varieties of dimension ≥ 3.