Very ample linear systems on abelian varieties
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Let $(X,L)$ be a polarized complex abelian variety of dimension $g$ where $L$ is a polarization of type $(1,...,1,d)$. For $(X,L)$ genberic we prove the following:
(1) If $d \ge g+2$, then $ϕ_L\colon X \to {\bf P}^{d-1}$ defines a birational morphism onto its image.
(2) If $d > 2^g$, then $L$ is very ample.
We show the latter by checking it on a suitable rank-$(g-1)$-degeneration.
29 pages, typeset with AMS-LaTeX 1.1
29 pages, typeset with AMS-LaTeX 1.1