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Feb 9, 2016 at 14:37 vote accept Lev Borisov
Dec 5, 2013 at 1:21 history edited Will Sawin CC BY-SA 3.0
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Dec 5, 2013 at 1:09 comment added Lev Borisov The funny thing is that $\overline M_{1,1}$ is definitely toric, but $M_{1,1}$ is not! The point at infinity that corresponds to the nodal curve is not torus invariant (the torus action is not particularly natural). I understand your argument about the fibers having (in general) four stacky points. So the best one can hope for is that the coarse moduli space is a toric surface. That seems plausible.
Dec 4, 2013 at 23:15 history answered Will Sawin CC BY-SA 3.0