Pushforwards of klt pairs under morphisms to abelian varieties

Abstract

Let $f$ be a morphism from a klt pair $(X,\Delta )$ to an abelian variety $A$, $m\ge 1$ a rational number and $D$ a Cartier divisor on $X$ such that $D{\sim }_{\mathbb{Q}}m(K_X+\Delta )$. We prove that the sheaf $f_{\ast }{\mathcal{O}}_X(D)$ becomes globally generated after pullback by an isogeny and has the Chen-Jiang decomposition, along with some related results. These are applied to some effective results for ${\mathcal{O}}_X(D)$ when $X$ is irregular.

29 pages

Cited by in corpus (4)

• Kodaira dimension of fibrations over abelian varieties
• Chen-Jiang decompositions for projective varieties, without Hodge modules
• On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture
• Estimates on the Kodaira dimension for fibrations over abelian varieties