Abstract
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.
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