{"paper":{"title":"Pointed Evaluation Fibers of Rational Curves on del Pezzo Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ari Krishna","submitted_at":"2026-06-29T17:42:56Z","abstract_excerpt":"Let $X$ be a Picard-rank-one del Pezzo manifold of dimension $n\\geq 4$ over an algebraically closed field of characteristic zero. Okamura proved that the unpointed Kontsevich spaces $\\overline{M}_{0,0}(X,d)$ are irreducible of the expected dimension for every $d\\geq 1$. We refine this result by studying pointed evaluation fibers. First, we prove that for every $d\\geq 1$, the one-pointed evaluation morphism $\\overline{M}_{0,1}(X,d)\\to X$ has geometrically irreducible generic fiber. Second, in the very ample cases $H^n=3,4,5$, we prove that for every $d\\geq 2$, the two-pointed evaluation morphis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30605","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30605/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"}