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

Christopher Hacon; Mihnea Popa; Christian Schnell

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arXiv · 1611.08768

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

Christopher Hacon·Mihnea Popa·Christian Schnell

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Abstract

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).

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Christopher Hacon, Mihnea Popa, Christian Schnell. 2016-11-27. Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun. https://arxiv.org/abs/1611.08768

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