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Questions tagged [torus-action]

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10
votes
0answers
205 views

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 \...
7
votes
0answers
359 views

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
votes
0answers
107 views

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
0answers
77 views

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
votes
0answers
308 views

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
vote
0answers
66 views

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
votes
0answers
116 views

Is $k$-diagonalizable element in split maximal torus of $G(k)$?

let $k$ be any field of char 0. $G$ is split reductive algebriac 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
votes
0answers
315 views

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 ...