Large families of stable bundles on abelian varieties

Abstract

A sequence of μ \mu -stable bundles { E m } \{E_m\} on a polarized variety ( X , H ) (X,H) is said to be a large family if their ranks and the discriminants become arbitrarily large as m m goes to infinity. We prove the existence of large families on a principally polarized abelian variety ( X , Θ ) (X,\Theta ) such that the Neron-Severi group is generated by Θ \Theta .