Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun

By Christopher D. Hacon, Mihnea Cristian Popa, C. Schnell. 2016

109 citations recorded by the source corpus.

We present a simplified proof for a recent theorem by Junyan Cao and Mihai Paun, confirming a special case of Iitaka's conjecture: if $f \colon X\to Y$ is an algebraic fiber space, and if the Albanese mapping of $Y$ is generically finite over its image, then we have the inequality of Kodaira dimensions $\kappa (X)\geq \kappa (Y)+\kappa (F)$, where $F$ denotes a general fiber of $f$. We include a detailed survey of the main algebraic and analytic techniques, especially the construction of singular hermitian metrics on pushforwards of adjoint bundles (due to Berndtsson, Paun, and Takayama).

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/feadcb0e87858e639860db0c310c7afc441b6999

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In Geometry and Topology

1. A. Höring
2. Junyan Cao

In Mathematical Physics

1. A. Höring
2. Junyan Cao

Citations in the corpus

• A decomposition theorem for projective manifolds with nef anticanonical bundle (2017, methodology): “We refer to [BP08, PT14, Rau15, Pău16, HPS16] for more details.”