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Toric variety is embedding of algebraic tori.
10
votes
1
answer
815
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Triangulations of polytopes and tilings of zonotopes
Consider a set $A = \{ a_1,a_2,\ldots, a_n \} $ of vectors in $\mathbb{R}^d$, which lie in a common affine hyperplane. Two convex polytopes may be obtained from $A$, namely the convex hull of the vect …
5
votes
0
answers
303
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Which (polytopal) fans/polytopes are secondary?
Let $P$ be a (d-1)-dimensional polytope with $n$ vertices that sits in an affine hyperplane in $\mathbb{R}^d$.
The secondary fan of $P$ is a polytopal fan in $\mathbb{R}^n$ with $d$-dimensional line …
4
votes
1
answer
196
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Toric ideal of slice of a polytope?
Given a collection $A:=\{a_1, \ldots ,a_n \}$ of different integer points in $\mathbb{N}^d$, which span an affine hyperplane when viewed in $\mathbb{R}^d$, one can define a toric ideal $I_A$ from a mo …
5
votes
Accepted
Triangulations of polytopes and tilings of zonotopes
Triangulations of polytopes are "more fundamental" than cubical tilings of zonotopes. By the Cayley trick, every cubical tiling of a zonotope can be seen as a triangulation of the Cayley lifting of th …