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Ben McKay
Ben McKay
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One question about About the connection between repellents and attractors under a $\mathbb{C}^{*}$ action on projective variety. ona projective variety

Let $X$ be a smooth projective variety with an action of $\mathbb{C}^{*}$. Let us suppose that the set $X^{\mathbb{C}^{*}}$ is finite. For $x \in X^{\mathbb{C}^{*}}$, let $A_{x}$ denote the attractor (under our $\mathbb{C}^{*}$-action) to $x$ and let $R_{x}$ denote the repellent. Question is the following: takeTake $x_{1}, x_{2} \in X^{\mathbb{C}^{*}}$ suppose $x_{2} \in \bar{A_{x_{1}}}$. Suppose that (where$x_{2} \in \bar{A}_{x_{1}}$, where $\bar{A_{x_{1}}}$$\bar{A}_{x_{1}}$ is the closure of $A_{x_{1}}$).

Is that true that $x_{1} \in \bar{R_{x_{2}}}$$x_{1} \in \bar{R}_{x_{2}}$?

One question about connection between repellents and attractors under $\mathbb{C}^{*}$ action on projective variety. on projective variety

Let $X$ be a smooth projective variety with an action of $\mathbb{C}^{*}$. Let us suppose that the set $X^{\mathbb{C}^{*}}$ is finite. For $x \in X^{\mathbb{C}^{*}}$ let $A_{x}$ denote the attractor (under our $\mathbb{C}^{*}$-action) to $x$ and let $R_{x}$ denote the repellent. Question is the following: take $x_{1}, x_{2} \in X^{\mathbb{C}^{*}}$ suppose $x_{2} \in \bar{A_{x_{1}}}$ (where $\bar{A_{x_{1}}}$ is the closure of $A_{x_{1}}$).

Is that true that $x_{1} \in \bar{R_{x_{2}}}$?

About the connection between repellents and attractors under a $\mathbb{C}^{*}$ action on a projective variety

Let $X$ be a smooth projective variety with an action of $\mathbb{C}^{*}$. Let us suppose that the set $X^{\mathbb{C}^{*}}$ is finite. For $x \in X^{\mathbb{C}^{*}}$, let $A_{x}$ denote the attractor (under our $\mathbb{C}^{*}$-action) to $x$ and let $R_{x}$ denote the repellent. Take $x_{1}, x_{2} \in X^{\mathbb{C}^{*}}$. Suppose that $x_{2} \in \bar{A}_{x_{1}}$, where $\bar{A}_{x_{1}}$ is the closure of $A_{x_{1}}$.

Is that true that $x_{1} \in \bar{R}_{x_{2}}$?

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Din
Din
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One question about connection between repellents and attractors under $\mathbb{C}^{*}$ action on projective variety. on projective variety

Let $X$ be a smooth projective variety with an action of $\mathbb{C}^{*}$. Let us suppose that the set $X^{\mathbb{C}^{*}}$ is finite. For $x \in X^{\mathbb{C}^{*}}$ let $A_{x}$ denote the attractor (under our $\mathbb{C}^{*}$-action) to $x$ and let $R_{x}$ denote the repellent. Question is the following: take $x_{1}, x_{2} \in X^{\mathbb{C}^{*}}$ suppose $x_{2} \in \bar{A_{x_{1}}}$ (where $\bar{A_{x_{1}}}$ is the closure of $A_{x_{1}}$).

Is that true that $x_{1} \in \bar{R_{x_{2}}}$?