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Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun by Hacon, Christopher; Popa, Mihnea; Schnell, Christian is a scholarly article available to read on EtoBox.

What is Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun about?

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).

Author

Hacon, Christopher; Popa, Mihnea; Schnell, Christian

Published

2016

Language

EN