{"paper":{"title":"On del Pezzo elliptic varieties of degree $\\leq 4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Luigi Tironi, Antonio Laface, Luca Ugaglia","submitted_at":"2015-09-30T15:25:39Z","abstract_excerpt":"\\special{html:<a href=\"hrefstring\">} Let $Y$ be a del Pezzo variety of degree $d\\leq 4$ and dimension $n\\geq 3$, let $H$ be an ample class such that $-K_Y=(n-1)H$ and let $Z\\subset Y$ be a $0$-dimensional subscheme of length $d$ such that the subsystem of elements of $|H|$ with base locus $Z$ gives a rational morphism $\\pi_Z\\colon Y\\dashrightarrow{\\mathbb P}^{n-1}$. Denote by $\\pi\\colon X\\to {\\mathbb P}^{n-1}$ the elliptic fibration obtained by resolving the indeterminacy locus of $\\pi_Z$. Extending the results of [arXiv:1305.3340] we study the geometry of the variety $X$ and we prove that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09220","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"}