Classifying smooth lattice polytopes via toric fibrations
TLDR
In this article, it was shown that any smooth Q-normal lattice polytope P of dimension n and degree d is a strict Cayley Polytope if n⩾2d+1.About:
This article is published in Advances in Mathematics.The article was published on 2009-09-10 and is currently open access. It has received 29 citations till now. The article focuses on the topics: Uniform k 21 polytope & Regular polytope.read more
Citations
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A simple combinatorial criterion for projective toric manifolds with dual defect
Alicia Dickenstein,Benjamin Nill +1 more
TL;DR: In this paper, it was shown that any smooth lattice polytope with codegree greater or equal than (1, 2) is a dual defective projective toric manifold.
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Polyhedral adjunction theory
TL;DR: In this article, a combinatorial view on the adjunction theory of toric varieties is presented, where two convex-geometric notions, namely the Q-codegree and the finite value of a rational polytope P, are explored.
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Algebro-geometric characterization of Cayley polytopes
TL;DR: In this paper, an algebro-geometric characterization of Cayley polytopes with lattice width one was given, where the Seshadri constants were used.
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Multi-Rees algebras and toric dynamical systems
TL;DR: In this paper, the relation between multi-Rees algebras and ideals that arise in the study of toric dynamical systems from the theory of chemical reaction networks is explored.
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Ehrhart Theory of Spanning Lattice Polytopes
TL;DR: In this article, it was shown that the Ehrhart theory of lattice polytopes has no gaps, i.e., a spanning polytope is a polyhedron whose lattice points affinely span the ambient lattice.
References
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Book
Lectures on Polytopes
TL;DR: In this article, the authors present a rich collection of material on the modern theory of convex polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids).
Book
The Adjunction Theory of Complex Projective Varieties
TL;DR: The Mathematical Expositions series as discussed by the authors is a collection of abstractions of pure and applied mathematics, focusing on methods and ideas essential to the topics in question, as well as their relationships to other parts of mathematics.
Book ChapterDOI
Decomposition of Toric Morphisms
TL;DR: In this article, the authors apply the ideas of Mori theory to toric toric varieties and show that the cone of effective 1-cycles NE(X) is polyhedral (1.7), spanned by the 1-strata l w ⊂ X.