Timeline for Automorphisms of a weighted projective space

7 events

when toggle format	what		by	license	comment
Nov 3, 2013 at 22:21	vote	accept	Puzzled
Jul 7, 2011 at 16:17	comment	added	Sasha		They are not isomorphic.
Jul 7, 2011 at 15:03	comment	added	Puzzled		The weighted projective plane $\mathbb{P}(2,3,4)$ is ismorphic to $\mathbb{P}(1,2,3)$. Following your method I find different automorphisms for $\mathbb{P}(1,2,3)$ and $\mathbb{P}(2,3,4)$. Where am I wrong ?
Jun 13, 2011 at 13:52	comment	added	mrw		ok. Thanks for the explanation. I also wanted to mention that the OP asked a slight different. He is asking what are the automorphisms that fix a smooth fixed point p.
Jun 12, 2011 at 19:53	comment	added	Sasha		I consider the weighted projective space as the quotient stack of a vector space (minus zero) by the torus action. This is not the same as a quotient in the category of schemes, and so the automorphism group is different. In your example, the quotient stack is $P^1$ but with an orbifold $Z/2Z$ point. The automorphism group should preserve the point. If you compare the subgroup of $PGL(2)$ preserving a point to the group analogous to the one in my answer you will see they are the same.
Jun 12, 2011 at 19:08	comment	added	mrw		I am a bit confused about this. Consider $\mathbb P(1,2)$. This should be the same as $\mathbb P^1$. So the automorphism group is $\mathbb PGL(2)$. But with the method you describe, wouldn't you get a different answer?
Jun 9, 2011 at 19:19	history	answered	Sasha	CC BY-SA 3.0