All Questions
Tagged with resolution-of-singularities toric-varieties
10 questions
3
votes
0
answers
138
views
Inverse image Weil divisor on a toric variety as a Cartier divisor
Let $X$ be a normal toric variety over an algebraically closed field and let $D$ be a torus invariant (prime) divisor. Assume $\pi\colon \tilde{X}\rightarrow X$ is a toric resolution of singularities ...
- 337
2
votes
0
answers
85
views
Is toroidalization local?
Let $f:X \to Y$ be a surjective morphism of smooth projective varieties, $D$ be a simple normal crossings divisor on $X$ and $U_Y \subset Y$ be an open subset over which $(X,D)$ is log smooth (in the ...
- 393
2
votes
0
answers
224
views
Log canonical centers of toric (and toroidal) varieties
Q1: Let $(X,B)$ be a toric variety. There exists a toric resolution of singularities $f:(Y,E) \to (X,B)$. Here is my question:
Is any lc center of $(X,B)$ an irreducible component of an intersection ...
- 393
1
vote
0
answers
178
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Birational model of a log smooth pair
Given a log smooth pair $(X,B)$ with a reduced boundary divisor $B$, consider a birational model $\pi:X' \to X$ and a boundary divisor $B'$ which is given by $K_{X'}+B'=\pi^*(K_X+B)$. Here is my ...
- 393
4
votes
0
answers
320
views
Toric Fan for the Du Val's singularities D_n and E_n
Let us consider the Du Val's singularities.
i.e. https://en.wikipedia.org/wiki/Du_Val_singularity.
It is well known that they are classified by ADE, because the exceptional divisors arising in the ...
- 489
2
votes
1
answer
180
views
Locally toric resolutions of compactifications
Suppose $U$ is a smooth, open $n$-dimensional variety over $\mathbb{C}.$ Say $X, X'$ are two proper normal-crossings compactifications of $U$. Call a map $m: X'\to X$ a modification if it is an ...
- 7,972
4
votes
1
answer
107
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When does a discrepant toric resolution induce a crepant resolution of a subvariety?
Let $Y$ be a complete intersection in a complete simplicial toric variety $X_\Sigma$ such that $\DeclareMathOperator{Sing}{Sing}\Sing(Y)\subset\Sing(X_\Sigma)$. Suppose that $\phi:X_{\widehat{\Sigma}}\...
5
votes
1
answer
172
views
Resolving $\mathbb Z_n$ action on $\mathbb C^2$
Consider a diagonal action of $\mathbb Z_n$ on $\mathbb C^2$ generated by $(z_1,z_2)\to (\mu^pz_1,\mu^qz_2)$, with $\mu^n=1$.
Question. Is it always possible to find a smooth blow up $X\to \mathbb ...
- 14.3k
2
votes
0
answers
116
views
Constructive Resolution of Toric Singularities via Model Theory
Do there exists some language $\mathcal{L}$ of rational polyhedral cones in rational vector spaces and a theory $T$ over $\mathcal{L}$ whose models $\mathcal{M}$ are resolutions of toric singularities?...
- 1,595
3
votes
0
answers
531
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"Step-by-Step" toric resolution process?
WLOG the fan $\Sigma$ of our toric variety $X_{\Sigma}$ is simplicial. (So $X_{\Sigma}$ has at worst orbifold singularities and all cones $\sigma \in \Sigma$ are simplicial).
The classical toric ...
- 1,939