Abstract: On abelian varieties it is possible to extend the notion of base point freeness (as well as other holomorphic properties) to rational multiples of polarizations. It is therefore natural to consider the base point freeness threshold of a given polarization L, namely the infimum of all rational numbers x such that xL is base point free. I will report on recent and less recent methods and results, due to various authors, on this invariant.
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