Timeline for Weighted projective spaces as stacks
Current License: CC BY-SA 3.0
3 events
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Feb 7, 2016 at 11:01 | comment | added | Lennart Meier | For me, a weighted projective (stacky) line is the stack quotient quotient $(Spec K[x,y]-0)/\mathbb{G}_m$, where $\mathbb{G}_m$ acts by $\lambda^a$ on $x$ and by $\lambda^b$ on $y$ for some weights $a,b\in\mathbb{Z}_{>0}$. We are in the world of the linked paper if $a$ and $b$ are coprime (no generic stabilizer). Now note that $\mathbb{Z}w\oplus \mathbb{Z}z/(aw = bz) \cong \mathbb{Z}$ with generator $cw+dz$, where $cb+ad = 1$. Thus, in the intersection of the two concepts, we get the same answer for $Pic$. | |
Feb 5, 2016 at 18:45 | comment | added | pbelmans | Is there a difference in terminology for weighted projective line or Picard group that explains why you say the Picard group is $\mathbb{Z}$ whereas e.g. section 2 of arxiv.org/abs/1409.7050v1 says that is a bit bigger than that? | |
Feb 1, 2016 at 18:17 | history | answered | Lennart Meier | CC BY-SA 3.0 |