Timeline for Are non-isomorphic covers of riemann surfaces also generally nonisomorphic as riemann surfaces?
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| Aug 20, 2013 at 5:16 | comment | added | Will Sawin | I'm concidering holomorphic maps. By a coincidence I just mean a pair of nonisomorphic covers that are isomorphic Riemann surfaces. By a space of covers, I mean a space of covers w/ the data of the ramification map. By "space of maps of any individual element", I mean for each element of this moduli space, which defines a curve, we consider the space of holomorphic maps from that curve to the base curve. | |
| Aug 14, 2013 at 11:31 | comment | added | Will Chen | Can you be more specific about what you mean by "coincidence", and exactly what kinds of maps you're talking about? (holomorphic maps, homeomorphisms...etc). By a space of covers, are you referring to the Riemann moduli space of X? (ie, $\mathcal{M}_g$ if $X$ has genus $g$?) Do covers in your space of covers include the data of the covering map? By "space of maps of any individual element", do you mean maps from the cover to $E$? or do you mean deck transformations of the given cover? | |
| Aug 11, 2013 at 16:45 | history | answered | Will Sawin | CC BY-SA 3.0 |