### Abstract

We present a simplified proof for a recent theorem by Junyan Cao and Mihai Păun, confirming a special case of Iitaka’s C_{n,m} conjecture: if f X → 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 κ(X) ≥ κ(Y) + κ(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, Păun, and Takayama).

Original language | English (US) |
---|---|

Title of host publication | Contemporary Mathematics |

Publisher | American Mathematical Society |

Pages | 143-195 |

Number of pages | 53 |

DOIs | |

State | Published - Jan 1 2018 |

### Publication series

Name | Contemporary Mathematics |
---|---|

Volume | 712 |

ISSN (Print) | 0271-4132 |

ISSN (Electronic) | 1098-3627 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun'. Together they form a unique fingerprint.

## Cite this

Hacon, C., Popa, M., & Schnell, C. (2018). Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun. In

*Contemporary Mathematics*(pp. 143-195). (Contemporary Mathematics; Vol. 712). American Mathematical Society. https://doi.org/10.1090/conm/712/14346