Cohomological rank functions and syzygies of projective bundles on abelian varieties

We use Jiang–Pareschi’s cohomological rank functions and techniques developed by Caucci and Ito to study syzygies of projective bundles on abelian varieties. Consequently, we generalize and refine Chiantipalli’s results regarding property $N_p$ of projective bundles over abelian varieties.