- Automorphisms of the Riemann Sphere - Math3ma
Theorem: Every automorphism f f of the Riemann sphere ^C C ^ is of the form f (z) = az+b cz+d f (z) = a z + b c z + d where a,b,c,d ∈ C a, b, c, d ∈ C such that ad − bc ≠ 0 a d b c ≠ 0
- Math 213b (Spring 2005) Yum-Tong Siu THE THEOREM OF RIEMANN-ROCH AND . . .
div f = mνPν − nνQν f is a meromorphic form and the sum of the residues of any meromorphic form on a compact Riemann s rface is zero We can also define the divisor div α of a meromorphic form on a Rie-mann surface in the same way Suppose P1, · · · , Pk are all the zeroes of � , mk k l div α =
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