{"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. Let $\\mathbb{C}^2 \\subset X$ be a compactification of $\\mathbb{C}^2$ where $X$ is a smooth rational compact surface and such that there exists a morphism of varieties $\\Phi :X\\to \\mathbb{P}^1$ which extends $f$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02462","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":""},"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"}