Angehrn-Siu-Helmke’s method applied to abelian varieties

Abstract We apply Angehrn-Siu-Helmke’s method to estimate basepoint freeness thresholds of higher dimensional polarized abelian varieties. showed that a conjecture Caucci holds for very general varieties in the moduli spaces $\mathcal {A}_{g, l}$ with only finitely many possible exceptions primitive polarization types l each dimension g . improved bound any $4$ -folds and simple $5$ -folds.