Questions tagged [torus-action]
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12
questions with no upvoted or accepted answers
11
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249
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Can the orbit with respect to a rotation on the torus hit an algebraic variety infinitely often?
Question: Does there exist a $d$-tuple $\alpha = (\alpha_1,\dots,\alpha_d) \in \mathbb{R}^d$ (with $1,\alpha_1, \dots,\alpha_d$ linearly independent over $\mathbb{Q}$) and an algebraic variety $V \...
8
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279
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Does Borel fixed-point theorem hold for Deligne-Mumford stacks?
Let $X$ be a proper Deligne-Mumford stack over $\mathbb{C}$ with an action by a complex torus $T$. Let $X^T$ denote the fixed locus.
Question: Is the following statement true?
...
7
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374
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The scheme-theoretic flow-in locus
Let $R$ be a ring with an $\mathbb{N}\times\mathbb{Z}$-grading. The $\mathbb{N}$-grading allows you to construct the scheme $X = \operatorname{Proj} R$, and the $\mathbb{Z}$-grading defines an action ...
4
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132
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Singular schemes with a torus action and embedded points
I've got a couple rather geometric questions about the following setup.
Let $X$ be a scheme over an algebraically closed field ($\mathbb{C}$, say) with the action of a torus $T$, such that the action ...
4
votes
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117
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Twisting stable maps to C* equivariant space by a line bundle
Let $X$ be a $\mathbb{C}^*$-equivariant algebraic variety. Then there is a notion of a map to $X$ twisted by a line bundle. Namely, let $B$ be a variety and $L/B$ a line bundle. Let $P_L=L\setminus B$...
3
votes
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90
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Decompositions from torus actions and compactness of (sub-)level sets
Let $T=\mathbb{C}^{*}$ act on a smooth complex quasi-projective variety $X$. Assume that the limit point $\lim_{t\to 0}t\cdot x$ exists for every $x\in X$.
From the induced $U(1)$-action and its (...
2
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0
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170
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Understanding the proof of a theorem by Van Den Bergh
I'm trying to understand the proof of a theorem by Van Den Bergh, which is Proposition 6 in the paper Bessenrodt, Christine and Lieven Le Bruyn. “Stable rationality of certain PGLn-quotients.” ...
2
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169
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Determining a toric GIT quotient
Consider the following $G = (\mathbb{C}^*)^{\times 3}$-action on $\mathbb{A}^6$:
$(\lambda_0,\lambda_1,\lambda_2) \cdot (x_0,x_1,x_2,y_0,y_1,y_2) = (\lambda_0x_0,\lambda_1x_1,\lambda_2x_2,\frac{\...
2
votes
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360
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Are schematic fixed points of a torus action on an affinized twistor deformation flat?
This is a follow-up to some earlier questions about flatness of schematic fixed points of certain deformations. Since I could never come up with good enough hypotheses in those examples, let me try a ...
1
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84
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How can I compute minimal distance of the AG-code on the Hirzebruch surface $\mathbb{F}_3$?
Let $\mathbb{F}_3$ be the Hirzebruch surface (with index $3$) over a finite field $\mathbb{F}_q$ and $\pi\!: \mathbb{F}_3 \to \mathbb{P}^1$ be the unique $\mathbb{P}^1$-fibration on $\mathbb{F}_3$. ...
0
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145
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Is $k$-diagonalizable element in split maximal torus of $G(k)$?
let $k$ be any field of char 0. $G$ is split reductive algebraic group over k. Let p in
G(k) be k-diagonalizable. Does there exist a split maximal torus of G(k) containing p?
I know that is ture for ...
0
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437
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Lifting of torus action to line bundle
Let $\mathbb{P}(V) = \mathbb{P}(\mathbb C \oplus \mathbb C)$ be with a $\mathbb C^*$ action : $\lambda (u,v) = (u,\lambda v)$.
There are two fixed points of this action, say $0$ and $\infty$. What ...