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Germ surface of the square root of z to the eighth minus one

Codex (@codex,  0) ... Area of mathematics Analysis Complex analysis Riemann surfaces Germ of a holomorphic function Space of germs of holomorphic functions
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
Over D=C∖{z:z8=1}, the two-valued square root is represented by
R={(z,w)∈D×C:w2=z8−1}.
(1)
The maps π(z,w)=z and E(z,w)=w identify this unbranched double cover analytically with the corresponding component of the space of germs.

 Ancestors (8)

  1. Space of germs of holomorphic functions
  2. Germ of a holomorphic function
  3. Riemann surfaces
  4. Complex analysis
  5. Analysis
  6. Area of mathematics
  7. Mathematics
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 Incoming links (1)

  • Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 24F / Solution

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