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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.09220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-30T15:25:39Z","cross_cats_sorted":[],"title_canon_sha256":"1084f38f12c10fb46e494d6344e654d76c6788f5ea1b5f0cd2578322e1e776fe","abstract_canon_sha256":"14914c3611eff660012e06a0592fabb783c14440d4fc0098e4549da0e492f132"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:26.800698Z","signature_b64":"g8FLD+RbLaImuQjFCyDijMAKChyimXt+w5vHdvu+3+WPTFTd7sdVfNCQ39ImvOCAonWSUmOwC+9zPwgbcANFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72827f3e83c60a9f52c539ae2ae4572de97bc84125d1543576d4a84bc2c6a6e3","last_reissued_at":"2026-05-18T01:31:26.800122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:26.800122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1509.09220","created_at":"2026-05-18T01:31:26.800221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.09220v1","created_at":"2026-05-18T01:31:26.800221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.09220","created_at":"2026-05-18T01:31:26.800221+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKBH6PUDYYFJ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKBH6PUDYYFJ6UWF","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKBH6PUD","created_at":"2026-05-18T12:29:34.919912+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX","json":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX.json","graph_json":"https://pith.science/api/pith-number/OKBH6PUDYYFJ6UWFHGXCVZCXFX/graph.json","events_json":"https://pith.science/api/pith-number/OKBH6PUDYYFJ6UWFHGXCVZCXFX/events.json","paper":"https://pith.science/paper/OKBH6PUD"},"agent_actions":{"view_html":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX","download_json":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX.json","view_paper":"https://pith.science/paper/OKBH6PUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.09220&json=true","fetch_graph":"https://pith.science/api/pith-number/OKBH6PUDYYFJ6UWFHGXCVZCXFX/graph.json","fetch_events":"https://pith.science/api/pith-number/OKBH6PUDYYFJ6UWFHGXCVZCXFX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX/action/storage_attestation","attest_author":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX/action/author_attestation","sign_citation":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX/action/citation_signature","submit_replication":"https://pith.science/pith/OKBH6PUDYYFJ6UWFHGXCVZCXFX/action/replication_record"}},"created_at":"2026-05-18T01:31:26.800221+00:00","updated_at":"2026-05-18T01:31:26.800221+00:00"}