Timeline for Quotient of a smooth curve by a finite group and differentials

8 events

when toggle format	what		by	license	comment
Dec 25, 2015 at 18:34	comment	added	Lisa S.		@NoamD.Elkies: I just mean that the action is "defined over $k$" as you say, i.e., $X$ is a $k$-scheme, $G$ is also a $k$-scheme (a "constant" one), there is a $k$-scheme morphism $G \times_k X \rightarrow X$ such that blah blah blah, etc.
Dec 25, 2015 at 4:24	comment	added	Noam D. Elkies		What does it mean for the action of $G$ on a curve to be "$k$-linear"? Or do you just mean that the action is defined over $k$?
Dec 24, 2015 at 19:30	vote	accept	Lisa S.
Dec 24, 2015 at 16:17	answer	added	Jason Starr		timeline score: 8
Dec 24, 2015 at 10:48	answer	added	Niels		timeline score: 7
Dec 24, 2015 at 8:09	comment	added	Philip Engel		Yes, the pullback of a form from the quotient is invariant, so you need only check that an invariant form is the pullback of a form. Given an invariant form on $X$, one can define a form locally on $Y$ away from the ramification locus by defining it as the value on one of the covering sheets. It is easy to check that this form extends holomorphically to all of $Y$. For instance, using Riemann-Hurwitz (or really just the local description of holomorphic maps $z\mapsto z^n$) to verify that the extension is holomorphic.
Dec 24, 2015 at 7:44	answer	added	R. van Dobben de Bruyn		timeline score: 4
Dec 23, 2015 at 21:40	history	asked	Lisa S.	CC BY-SA 3.0