Timeline for Lifting a morphism along quotient of a group action

6 events

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Aug 29, 2022 at 5:43	history	edited	user127776	CC BY-SA 4.0	added 164 characters in body
Aug 29, 2022 at 5:39	comment	added	user127776		@KhashF BTW I am not sure if that example contradicted anything since the $U$ mentioned above is an etale open not a Zariski open. Meaning if we consider etale covers it should be possible to make your map from $X$ to $\mathbb{CP}^1$ liftable. I think my mentioning of Zariski or analytical open has confused many people, I should remove that. What I meant, is that there are two types of topologies on the hom space which comes from the Hilbert scheme one is Zariski and the other one is analytic.
Aug 28, 2022 at 20:43	history	edited	user127776	CC BY-SA 4.0	added 172 characters in body
Aug 28, 2022 at 20:37	comment	added	user127776		@KhashF Thanks, yes this is not true in general I should add what $Y$ and $G$ are supposed to be.
Aug 28, 2022 at 20:28	comment	added	KhashF		What if we take $X$ and $Y$ to be compact Riemann surfaces with $g(X)<g(Y)$, and $Y$ admitting a Galois ramified cover $Y\rightarrow Y/G=\Bbb{CP}^1$? By the Riemann Existence Theorem, there exists a non-constant morphism $X\rightarrow \Bbb{CP}^1$, but there is no non-constant morphism from a non-empty Zariski open subset of $X$ to $Y$ since such a thing can be extended to a non-constant morphism $X\rightarrow Y$.
Aug 26, 2022 at 19:10	history	asked	user127776	CC BY-SA 4.0