All Questions
Tagged with toric-varieties fans
7
questions
3
votes
1
answer
141
views
A question related to the strong Oda conjecture
A fan is a collection of strongly convex rational polyhedral cones in $\mathbb Z^n$, which we often think of as contained in $\mathbb Q^n$ or $\mathbb R^n$ for purposes of visualizing it. The defining ...
- 6,210
2
votes
1
answer
313
views
Is the blowup of a toric variety corresponding to a subdivision normal?
Toroidal Embeddings 1 by KKMS say subdividing the fan of a toric variety yields the fan of a normalized blowup. How do I avoid normalization? Do I need to choose my subdivision carefully, or is it ...
- 1,084
2
votes
1
answer
159
views
Sections of Cartier divisors on toric varieties
Let $X_{\Sigma}$ be a projective toric variety. Consider the total coordinate ring
$$S = \mathbb{C}[x_{\rho}\: | \: \rho\in\Sigma(1)]$$
Define $\deg(x_{\rho}) = D_{\rho}$.
Now, take a divisor $D = \...
user75933
3
votes
1
answer
256
views
Relation between the number of maximal cones in a fan and the geometry of corresponding toric variety
It is well known that a (smooth complete) fan $\Delta$ corresponds to a (smooth proper) toric variety $X= X_\Delta$.
My question is whether there is a relationship between the number of maximal cones ...
- 95
2
votes
0
answers
277
views
Is there a "fundamental theorem of toric geometry"?
I have some questions about toric geometry.
1) Can any toric variety (I mean not necessarily smooth or projective, ...) be constructed from a fan ?
2) Suppose $T_1$ and $T_2$ are toric varieties ...
- 4,503
2
votes
2
answers
629
views
The boundary of toric varieties
Let $\mathcal{X}$ be a toric variety, with $T$ a torus embedded as an open set
in $\mathcal{X}$ (and where the algebraic action of $T$ extends to $\mathcal{X}$). As I am not a toric specialist at all, ...
- 4,503
4
votes
0
answers
281
views
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 ...
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