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Let $ \sim$ denote the equivalence relation on C^2\{(0,0)} given by

$(x,y)\sim(z,w) iff (x,y)=(2^nz,2^nw) \exists n

Let X= C^2\{(0,0)}/sim (This is a so-called ``Hopf surface'').

Determine the connected component Aut(X)^0 of the group of holomorphic automorphisms of $ X$.

Hint: Consider the map X -> P_1 given by (x,y) -> [x:y].

To be handed in until August, 31 2001.
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Joerg Winkelmann jwinkel@member.ams.org

Last modification: 18 Jul 2001