Some remarks on ample line bundles on abelian varieties (Q1077478): Difference between revisions

Let \({\mathcal L}\) be an ample line bundle on an abelian variety A. If (A,\({\mathcal L})\) is not isomorphic to \((A_ 1\times A_ 2\), \({\mathcal O}(D_ 1\times A_ 2+A_ 1\times D_ 2))\) where \(A_ i\) \((i=1,2)\) is an abelian variety of positive dimension, \(D_ i\) is an ample divisor on \(A_ i\) \((i=1,2)\) and dim \(\Gamma\) (A\({}_ 1,{\mathcal O}(D_ 1))=1\), and if dim \(\Gamma\) (A,\({\mathcal L})\geq 2\), then \({\mathcal L}^{\otimes 2}\) is very ample.