On the global generation of direct images of pluri-adjoint line bundles

Abstract

We study the Fujita-type conjecture proposed by Popa and Schnell. We obtain an effective bound on the global generation of direct images of pluri-adjoint line bundles on the regular locus. We also obtain an effective bound on the generic global generation for a Kawamata log canonical $\mathbb{Q}$-pair. We use analytic methods such as $L^2$ estimates, $L^2$ extensions and injective theorems of cohomology groups.

8 pages, v2: the abstract and introduction were changed, v3: completely revised version, to appear in Mathematische Zeitschrift

References in corpus (1)

• Effective generation and twisted weak positivity of direct images

Cited by in corpus (2)

• Effective generation and twisted weak positivity of direct images
• Characterization of pseudo-effective vector bundles by singular Hermitian metrics