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 $f_* \omega_X^{\otimes m}$ 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.

中文翻译：

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态射下多子丛向阿贝尔簇的推进

令 $f \colon X \to A$ 是一个从平滑射影变体到阿贝尔变体（在复数域上）的态射。我们表明，滑轮 $f_* \omega_X^{\otimes m}$ 在同基因拉回后成为全局生成的。当 $m \ge 2$ 时，我们用它来推导出这些束的分解定理，类似于当 $m = 1$ 时 Chen-Jiang 得到的。这反过来又适用于具有规范奇点的不规则变体的多规范线性级数的有效结果。