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Title: On the bicanonical map of irregular varieties
Author: Barja Yáñez, Miguel Ángel
Lahoz Vilalta, Martí
Naranjo del Val, Juan Carlos
Pareschi, Giuseppe
Keywords: Geometria algebraica
Algebraic geometry
Issue Date: 27-Jul-2012
Publisher: University Press
Abstract: 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.
Note: Versió postprint del document publicat a:
It is part of: Journal of Algebraic Geometry, 2012, vol. 21, p. 445-471
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ISSN: 1056-3911
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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