Picard-Zahlen komplexer Tori

We give explicit equations for the calculation of Chern classes of holomorphic line bundles on a complex torus X. As easy applications we deduce properties of the Picard numbers ρ(X) of n-dimensional tori, when the complex structure changes. The tori with ρ(X)≥k form a countable union of analytic subsets in a moduli space M; furthermore the set of tori with ρ(X)=k is empty or dense in M. For n-dimensional tori one has O≤ρ(X)≤n², but for n≥3 not all numbers 0≤k≤n² occur as Picard numbers. We conclude our considerations with a list of examples and with some remarks about this gap phenomenon in the distribution of Picard numbers of complex tori.