{"paper":{"title":"On the 10-web by conics on the quartic del Pezzo surface","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luc Pirio","submitted_at":"2024-01-12T17:20:00Z","abstract_excerpt":"We study and compare the webs $\\boldsymbol{\\mathcal W}_{{\\rm dP}_d}$ defined by the conic fibrations on a given smooth del Pezzo surface ${\\rm dP}_d$ of degree $d$ for $d=4$ and $d=5$. In a previous paper, we proved that for any positive $d\\leq 6$, the web by conics $\\boldsymbol{\\mathcal W}_{{\\rm dP}_d}$ carries a particular abelian relation ${\\bf HLog}_d$, whose components all are weight $7-d$ antisymmetric hyperlogarithms. The web $\\boldsymbol{\\mathcal W}_{{\\rm dP}_5}$ is a geometric model of the exceptional Bol's web and the relation ${\\bf HLog}_5$ corresponds to the famous `Abel's identity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.06711","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.06711/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}