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arXiv · 1705.01975

Pushforwards of pluricanonical bundles under morphisms to abelian varieties

Luigi Lombardi·Mihnea Popa·Christian Schnell
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Abstract

Let $f \colon X \to A$ be a morphism from a smooth projective variety to an abelian variety (over the field of complex numbers). We show that the sheaves $f_* ω_X^{\otimes m}$ become globally generated after pullback by an isogeny. We use this to deduce a decomposition theorem for these sheaves when $m \ge 2$, 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.

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Luigi Lombardi, Mihnea Popa, Christian Schnell. 2020-10-26. Pushforwards of pluricanonical bundles under morphisms to abelian varieties. https://doi.org/10.4171/jems%2F970

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