{"paper":{"title":"Algebraic fiber spaces over abelian varieties: around a recent theorem by Cao and Paun","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian Schnell, Christopher Hacon, Mihnea Popa","submitted_at":"2016-11-27T00:35:13Z","abstract_excerpt":"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)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08768","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}