All Questions
Tagged with toric-varieties cohomology
6
questions
7
votes
0
answers
264
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Cohomology of fibers of a morphism of a blowup of affine space
Consider $\mathbb A^n$ and let $\Sigma$ be a subdivision of its toric fan $\mathbb R^n_{\geq 0}$. This induces a toric blowup $\pi : Y \to \mathbb A^n$. Let $X \subseteq Y$ be the preimage of the ...
6
votes
1
answer
231
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Cohomology of toric blowup
Let $n\geq2$. Let $G$ be a linear automorphisms group of prime order on $\mathbb{C}^n$. We assume that $0$ is the unique fixed point of $G$.
I consider the quotient $\mathbb{C}^n/G$. It is a toric ...
1
vote
0
answers
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A regular sequence in a quotient by a "half lattice" defined by a toric manifold
I am interested in some properties of polynomial algebras associated with smooth compact toric varieties. Recall that a toric manifold can be obtained as a quotient $$P^{-1}(p) / \mathbb{K}$$ by the ...
2
votes
0
answers
62
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On cohomological algebras related to toric manifolds
I am interested in some cohomological algebras related to toric manifolds. We consider a toric manifold $M$ as a quotient
$$M = P^{-1}(p) / \mathbb{K}, \quad P : \mathbb{C}^n \to \text{Lie}(\mathbb{K})...
0
votes
0
answers
86
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On the dimension of the cohomology of toric manifolds
Let $M$ be a toric manifold. I'm not sure what conditions on $M$ are required, but one can assume, if needed, that it is compact, smooth, etc. We consider $M$ as a quotient given by the momentum map $...
5
votes
2
answers
897
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Cohomology of the toric variety $X_\Sigma=\mathbb C^2\sqcup \mathbb C^2\big/\left((x,y)_1\sim(x^{-1},y^{-1})_2\right)_{x,y\neq 0}$
I'm writing a thesis on Chow rings of toric varieties and am looking for a reference on the singular cohomology ring of the blowup of $\mathbb C^2$ at xy=0, i.e. at the coordinate axes. The ...