All Questions
Tagged with toric-varieties projective-geometry
8
questions
2
votes
1
answer
147
views
Intersection in toric variety
In a toric variety $T$ of dimension $11$ I have a subvariety $W$ of which I would like to compute the dimension.
On $T$ there is a nef but not ample divisor $D$ whose space of sections has dimension $...
- 133
1
vote
0
answers
65
views
Polytope of a projected toric variety
I was looking for such a result in the book by Cox, Little and Schenck but I'm not able to find a proper reference.
All of the following requirements are tacitly assumed to be in the projective ...
- 1,333
1
vote
2
answers
420
views
Embedding of a blow-up
In $\mathbb{P}^1\times\mathbb{P}^2$ take a general divisor $X$ of type $(0,2)$. Consider two general divisors $H_1,H_2$ of type $(2,1)$ and set $Y = X\cap H_1\cap H_2$.
Let $Z$ be the blow-up of $X$ ...
- 8,922
0
votes
0
answers
133
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Problem in calculating the global sections of $\mathcal{O}_{\mathbb{P}^3}(d)\otimes \mathcal{I}_Z$
This is an additional question to the one I posed in Equivalence of sequences of blowups of $\mathbb{P}^3$
Let $[x_1,x_2,x_3,x_4]$ be coordinates of $\mathbb{P}^3$ and $Z\subset \mathbb{P}^3$ the ...
- 1,333
2
votes
1
answer
228
views
Equivalence of sequences of blowups of $\mathbb{P}^3$
Let $[x_1,x_2,x_3,x_4]$ be coordinates of $\mathbb{P}^3$ and $Z\subset \mathbb{P}^3$ the subscheme given by the ideal $$I_Z=(x_1,x_2,x_3^2) \subset \mathbb{C}[x_1,x_2,x_3,x_4]$$ i.e. $Z$ is a double ...
- 1,333
4
votes
1
answer
594
views
Cohomology of divisors on Hirzebruch surfaces
Consider the Hirzebruch surface $\mathbb{F}_n = \mathbb{P}(\mathcal{O}_{\mathbb{P}^1}\oplus \mathcal{O}_{\mathbb{P}^1}(n))\rightarrow\mathbb{P}^1$. The Picard group of $\mathbb{F}_n$ is generated by ...
user114666
4
votes
3
answers
446
views
Existence of a morphism between two toric varieties
Does there exist a morphism between the blow-up of $\mathbb{P}^3$ in four general points and $\mathbb{P}^1\times\mathbb{P}^1$? If not why?
user68440
1
vote
0
answers
336
views
A question on the secondary fan
I am studying the secondary fan decomposition of the effective cone of a projective variety $X$. Let as assume that $X$ is a Mori Dream Space. As far as I understand passing from a cone of maximal ...
user61586