0 Abelian Varieties into 2 g + 1 - dim . Linear Systems
نویسنده
چکیده
We show that polarisations of type (1, ..., 1, 2g + 2) on g-dimensional abelian varieties are never very ample, if g ≥ 3. This disproves a conjecture of Debarre, Hulek and Spandaw. We also give a criterion for non-embeddings of abelian varieties into 2g + 1-dimensional linear systems.
منابع مشابه
0 Line bundles of type ( 1 , . . . , 1 , 2 , . . . , 2 , 4 , . . . , 4 ) on Abelian Varieties
We show birationality of the morphism associated to line bundles L of type 4) on a generic g−dimensional abelian variety into its complete linear system such that h 0 (L) = 2 g. When g = 3, we describe the image of the abelian threefold and from the geometry of the moduli space SU C (2) in the linear system |2θ C |, we obtain analogous results in IP H 0 (L).
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