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Put $\\mathcal{D}=X\\setminus \\mathbb{C}^2$; $\\mathcal{D}$ is a curve whose irreducible components are smooth rational compact curves and all its singularities are ordinary double points. The dual graph of $\\mathcal{D}$ is a tree. We are interested in this tree, and we analyse its complexity in terms of the genus of the generic fib"},"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":"1809.02462","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-07T13:29:51Z","cross_cats_sorted":[],"title_canon_sha256":"4781871104f76ff2340500d44468b11adaefea8e5362865568f96fb2dbf9437d","abstract_canon_sha256":"267f998dae67c402facd8132cbf66395e0b27ba0459f8ed8d62c7b4256270d33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:53.885191Z","signature_b64":"aomdoMWFUWDNWkdj5qcrlHDBDrWK6oOn+rnk/WweH8x1z01MFfi/Je0xymXmFs20632pVlY9g8mQXIINyLciBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30d3154a4dbb09fc2e4e059c29ba0fc396c62dd14d1565785092a4196b64a311","last_reissued_at":"2026-05-17T23:47:53.884629Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:53.884629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure of the Newton tree at infinity of a polynomial in two variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Daigle, Pierrette Cassou-Nogues","submitted_at":"2018-09-07T13:29:51Z","abstract_excerpt":"Let $f:\\mathbb{C}^2 \\to \\mathbb{C}$ be a polynomial map. 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