Line bundles of type (1,,,1,2,,,2,4,,,4) on Abelian Varieties

Details Line bundles of type (1,,,1,2,,,2,4,,,4) on Abelian Varieties Line bundles of type (1,,,1,2,,,2,4,,,4) on Abelian Varieties

2000-04-14

arxiv.org/abs/math/0004095v2

Mathematics

Algebraic Geometry

20 pages. Revised version

Scientific paper

We show birationality of the morphism associated to line bundles $L$ of type $(1,...,1,2,...,2,4,...,4)$ 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 $|2\theta_C|$, we obtain analogous results in $\p H^0(L)$.

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