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Very ample linear systems on abelian varieties. (English) Zbl 0806.14031
Let \((X,L)\) be a complex abelian variety of dimension \(g\) with a polarization of type \((1, \dots, 1,d)\). For \((X,L)\) generic we prove the following:
1. If \(d \geq g + 2\), then \(\varphi_{| L |} : X \to \mathbb{P}^{d- 1}\) 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.

14K05 Algebraic theory of abelian varieties
14C20 Divisors, linear systems, invertible sheaves
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