On the bicanonical map of irregular varieties

Details On the bicanonical map of irregular varieties On the bicanonical map of irregular varieties

2009-07-24

arxiv.org/abs/0907.4363v2

Mathematics

Algebraic Geometry

20 pages. There was an inaccuracy in the proof of Theorem 4.13. We have fixed the problem giving a slightly different proof. T

Scientific paper

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.

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