Timeline for Automorphisms of a specific type of weighted projective space

8 events

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Sep 28, 2012 at 16:58	comment	added	Jérémy Blanc		Thanks for editing, anyway the good point was to describe the isomorphism and action on $\mathbb{P}^{n-1}$. But it is funny that the kernel is quite strange and depends in fact on the roots of unity in $\mathbb{K}^*$.
Sep 28, 2012 at 14:02	history	edited	rita	CC BY-SA 3.0	added 128 characters in body; deleted 6 characters in body; added 26 characters in body
Sep 28, 2012 at 14:00	comment	added	rita		You are right, I had been too hasty. Thanks for pointing this out. I'll edit my answer.
Sep 28, 2012 at 12:25	comment	added	Jérémy Blanc		Pay attention that the kernel of the map $G\to \mathrm{PGL}(n,\mathbb{K})$ is not equal to $\mathbb{K}^*\times \mathbb{K}^{N+1}$. In fact is it not abelian: for example, the elements $(x_1:\dots:x_n:y)\mapsto(x_1:\dots:x_n:\alpha y)$ and $(x_1:\dots:x_n:y)\mapsto (x_1:\dots:x_n:y+(x_1)^k)$ do not commute in general. See below.
Sep 24, 2012 at 22:18	history	edited	rita	CC BY-SA 3.0	added 10 characters in body
Sep 24, 2012 at 15:46	vote	accept	Stanley Yao Xiao
Sep 24, 2012 at 7:31	history	edited	rita	CC BY-SA 3.0	edited body; added 92 characters in body
Sep 24, 2012 at 7:12	history	answered	rita	CC BY-SA 3.0