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Some remarks on ample line bundles on abelian varieties

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Let L be an ample line bundle on an abelian variety A. We show that L⊗2 is very ample if (A,L) is not isomorphic to (A1×A2,o(D1×A2+A1×D2)) where Ai is an abelian variety (i=1,2), Di is an ample divisor on Ai (i=1,2) and ℓ(A1,o(D1))=1, and if ℓ(A,L)≧2. As an application we show that L⊗2 is base point free if L is an ample line bundle on bielliptic surface.

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In conclusion, the author would like to thank the referee for very helpful advice.

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Ohbuchi, A. Some remarks on ample line bundles on abelian varieties. Manuscripta Math 57, 225–238 (1987). https://doi.org/10.1007/BF02218082

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  • DOI: https://doi.org/10.1007/BF02218082

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