Generic Vanishing Index and the Birationality of the Bicanonical Map of Irregular Varieties

Mathematics – Algebraic Geometry

Scientific paper

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10 pages, to appear in Mathematische Zeitschrift

Scientific paper

We prove that any smooth complex projective variety with generic vanishing
index bigger or equal than 2 has birational bicanonical map. Therefore, if X is
a smooth complex projective variety X with maximal Albanese dimension and
non-birational bicanonical map, then the Albanese image of X is fibered by
subvarieties of codimension at most 1 of an abelian subvariety of Alb X.

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