Linear systems on abelian varieties of dimension 2𝑔+1

Iyer, Jaya

doi:10.1090/S0002-9939-01-06264-5

Linear systems on abelian varieties of dimension $2g+1$
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by Jaya N. Iyer PDF

Proc. Amer. Math. Soc. 130 (2002), 959-962 Request permission

Abstract:

We show that polarisations of type $(1,...,1,2g+2)$ on $g$-dimensional abelian varieties are never very ample, if $g\geq 3$. 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.

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