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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"},"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":"2606.30605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-29T17:42:56Z","cross_cats_sorted":[],"title_canon_sha256":"4fa82efb42fcb5891cf198027a4b474aa44748fd0b5def834ded31d83816fcea","abstract_canon_sha256":"ad4c3901a84741e8db08127085537e361b5d104fe47902c19b40809abad6e013"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:22.388826Z","signature_b64":"aqO2GACFdgkmgzOCOm4A2sgWt/yQY+PE33b9SEXKyNkehkilvMhfGRqb0o0oL8oJTs955cr+4p3JOeXVaX0wAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1760932f10335ab8203ecc8d2a80180c11a6612ad600e2337c6eae0a5ede8e1","last_reissued_at":"2026-06-30T02:18:22.388175Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:22.388175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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