By Wolfgang Franz

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60). 25. 50). 63) comes from arithmetic quotients. 54). 31: Since the algebraic embedding M O c is open, the complement (lB/r)\(lBo/r) is algebraically closed in lB/r, hence an analytic subset (of dimension:::; 1). The quotient map lB ~ lB/r is locally finite. 31 follows immediately. The precise determination of lIllo C IIll needs finer methods. We refer to the next chapter for this purpose. Assume that this is done. 12. 21. Then it belongs to jo introduced at the beginning of this section. 63) teaches us that the moduli point of Jac(C) lies in the open part lBo/r of A;.

Let C be a (smooth, compact, complex) curve of positive genus g, 01, ... ,02g a normal basis of H 1 (C,Z) and w = (WI, ...

27. A holomorphic function f : lB\ ---.

### Algebraic topology by Wolfgang Franz

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