Let f : X -> A be a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). We show that the sheaves f(*)omega(circle times m)(X) become globally generated after pullback by an isogeny. We use this to deduce a decomposition theorem for these sheaves when m >= 2, analogous to that obtained by Chen-Jiang when m = 1. This is in turn applied to effective results for pluricanonical linear series on irregular varieties with canonical singularities.
Pushforwards of pluricanonical bundles under morphisms to abelian varieties / L. Lombardi, M. Popa, C. Schnell. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 22:8(2020), pp. 2511-2536. [10.4171/JEMS/970]
Pushforwards of pluricanonical bundles under morphisms to abelian varieties
L. Lombardi;
2020
Abstract
Let f : X -> A be a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). We show that the sheaves f(*)omega(circle times m)(X) become globally generated after pullback by an isogeny. We use this to deduce a decomposition theorem for these sheaves when m >= 2, analogous to that obtained by Chen-Jiang when m = 1. This is in turn applied to effective results for pluricanonical linear series on irregular varieties with canonical singularities.File | Dimensione | Formato | |
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