{"paper":{"title":"On birational trivial families and Adjoint quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Zucconi, Luca Cesarano, Luca Rizzi","submitted_at":"2019-03-15T00:34:19Z","abstract_excerpt":"Let $\\pi\\colon \\mathcal{X}\\to B$ be a family whose general fiber $X_b$ gives a $(d_1,...,d_a)$ polarisation of a general Abelian variety where $1\\leq d_i\\leq 2$, $i=1,...,a$ and $a\\geq 4$. We show that the fibers are in the same birational class if all the $(m,0)$ forms on $X_b$ are liftable to $(m,0)$ forms on $\\mathcal{X}$ where $m=1$ and $m=a-1$. Actually we show general criteria to find families with fibers in the same birational class, which leads together with a famous theorem of Nori to some interesting applications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06307","kind":"arxiv","version":1},"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"}