Positivity of twisted relative pluricanonical bundles and their direct images

By Mihai Puaun, S. Takayama. 2014

165 citations recorded by the source corpus.

Our main goal in this article is to establish a quantitative version of the positivity properties of twisted relative pluricanonical bundles and their direct images. The notion of "singular Hermitian metric" on vector bundles (together with an appropriate definition of positivity of the associated curvature) plays a major role here, and its properties are studied via a version of Ohsawa-Takegoshi extension theorem. Part of this article is based on the joint work of the first named author with Bo Berndtsson, and it can be seen as an expanded and updated version of it.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ebaf559fe23a331b2a4a7f8b97ad0e63bf2e741e

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Kodaira dimension of algebraic fiber spaces over abelian varieties (2015, unknown): “By [34], the restriction p (KX/Y + G)| 0 (5.”
A decomposition theorem for projective manifolds with nef anticanonical bundle (2017, methodology): “(ii): If X is projective, by using the same argument as in [PT14, Sect 2][Pău16, Thm 2.21], we can prove that the notion of "weakly positively curved vector bundle" implies the weak positivity in the sense of Viehweg.”
Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun (2016, methodology): “Here, one small improvement over [PT14] is the observation that these metrics are continuous on the Zariski-open subset of Y where f : X → Y is submersive.”