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I can show that for "generic" lattice $\Lambda$ in $\mathbb C^n$ for $n\ge2$, the complex tori $\mathbb C/\Lambda$ has only trivial meromorphic function. I want to deduce that on such tori, there is no divisor.

There is such an argument in Georges Elencwajg and Otto Forster's paper Vector bundles on manifolds without divisors and a theorem on deformations.

enter image description here See the second paragraph. Probably it is a well-known fact, but could someone give me some hint or reference? I appreciate it.

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