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We extend this result to generalized Severi varieties parametrizing plane curves which, in addition, satisfy tangency conditions of given orders with respect to a given line. We show that the degrees of these varieties, appropriately rescaled, are given by a combinatorially defined \"relative node polynomial\" in the tangency orders, provide"},"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":"1009.5063","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-26T05:35:21Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f666a960fa3a8d775e6f7ab8609998ba874cbcfbaeb7c11a382454286d88ab7e","abstract_canon_sha256":"38d22af94bea1329e7bb288a3db6d364f31ef7bafa78fd230e166903bf161dbb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:13.894559Z","signature_b64":"flkNnPNtJ8liYwEjoNETmBnHarF//aG88ZoJWv3FBTnCqsADbwyCwbc5Yj3KLWuGAsIR1ig6oT3MEVDLGQNODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aaa2a55bffba6843f29eab718ba2a015fbbcab84361132f05823d1b1d1dee24a","last_reissued_at":"2026-05-18T03:48:13.893784Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:13.893784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative Node Polynomials for Plane Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Florian Block","submitted_at":"2010-09-26T05:35:21Z","abstract_excerpt":"We generalize the recent work of S. 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