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nLab > Latest Changes: branched cover of Riemann sphere

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2014

    created a bare minimum at branched cover of Riemann sphere, just to record the fact that every compact connected Riemann surface admits this structure.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 22nd 2014

    I added some material (which I now see is also alluded to in a comment by David C. in a different thread) on the dual picture for field extensions. As for a reference: I thought this very classical correspondence between compact Riemann surfaces and field extensions of transcendence degree 1 was beautifully described in one of Mumford’s books (on abelian varieties?) – I wish to Christ that I could remember exactly. I used to have this book.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2014

    Thanks a whole lot!

    Probably Zhen Lin knows which book that is.

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 22nd 2014

    The title just flashed into my brain. It’s Curves and their Jacobians by Mumford. I can add that in.

1 to 4 of 4

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