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user 124705
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Weights on the linearization
Consider, just as an example, an action of $\mathbb{C}^*$ on $\mathbb{P}^2$ of the form
$$t\cdot p=[p_0:tp_1:t^2p_2]$$
There are $3$ fixed points, namely $e_1,e_2,e_3$. If I consider a $\mathbb{C}^*$- …
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