Algebraic fiber spaces over abelian varieties: Around a recent theorem by Cao and Păun

Christopher Hacon, Mihnea Popa, Christian Schnell

Research output: Chapter in Book/Report/Conference proceedingChapter

11 Scopus citations

Abstract

We present a simplified proof for a recent theorem by Junyan Cao and Mihai Păun, confirming a special case of Iitaka’s Cn,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 languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages143-195
Number of pages53
DOIs
StatePublished - Jan 1 2018

Publication series

NameContemporary Mathematics
Volume712
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

ASJC Scopus subject areas

  • Mathematics(all)

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    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