Let be a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). We show that the sheaves become globally generated after pullback by an isogeny. We use this to deduce a decomposition theorem for these sheaves when , analogous to that obtained by Chen–Jiang when . This is in turn applied to effective results for pluricanonical linear series on irregular varieties with canonical singularities.
Cite this article
Luigi Lombardi, Mihnea Popa, Christian Schnell, Pushforwards of pluricanonical bundles under morphisms to abelian varieties. J. Eur. Math. Soc. 22 (2020), no. 8, pp. 2511–2536DOI 10.4171/JEMS/970