Very ample invertible sheaves of new type on abelian varieties (Q1316487)

The author proves the following result (which is a generalization of a classical result due to Comessatti): Let \(A\) be an abelian variety over an algebraically closed field. Let \(L\) and \(M\) be two line bundles on \(A\) such that \(h^ 0 (A,L) = h^ 0 (A,M) = 1\). Write \(L \cong {\mathcal O}_ A (D)\) and \(M \cong {\mathcal O}_ A (E)\), with \(D\) and \(E\) positive divisors, and assume that each component of \(D\) is not algebraically equivalent to a component of \(E\). Then \(L \otimes M\) is very ample.