Lifting of torus action to line bundle - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T00:15:58Z http://mathoverflow.net/feeds/question/83270 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/83270/lifting-of-torus-action-to-line-bundle Lifting of torus action to line bundle tonywang 2011-12-12T19:18:27Z 2011-12-12T19:18:27Z <p>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 does this mean to equivariantly lift this action to a line bundle $L$ over $\mathbb P(V)$, by choosing the weights $[l_0, l_{\infty}]$ of the fibre representations $L_0, L_{\infty}$ at the fixed points?</p>