  From the point of view of uniform bounds for the birationality of
pluricanonical maps, irregular varieties of general type and maximal Albanese
dimension behave similarly to curves. In fact Chen-Hacon showed that, at least
when their holomorphic Euler characteristic is positive, the tricanonical map
of such varieties is always birational. In this paper we study the bicanonical
map. We consider the natural subclass of varieties of maximal Albanese
dimension formed by primitive varieties of Albanese general type. We prove that
the only such varieties with non-birational bicanonical map are the natural
higher-dimensional generalization to this context of curves of genus 2:
varieties birationally equivalent to the theta-divisor of an indecomposable
principally polarized abelian variety. The proof is based on the (generalized)
Fourier-Mukai transform.
