Projective normality and basepoint‐freeness thresholds of general polarized abelian varieties

Source abstract

Abstract For a polarized abelian variety , Z. Jiang and G. Pareschi introduce an invariant , called the basepoint‐freeness threshold. Using this invariant, we show that a general polarized abelian variety of dimension is projectively normal if and the type of is not . This bound is sharp since it is known that any polarized abelian variety of type is not projectively normal. We also give an application of to the infinitesimal Torelli theorem for .