{"paper":{"title":"Discrete Invariants of Generically Inconsistent Systems of Laurent Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Leonid Monin","submitted_at":"2017-03-19T05:23:33Z","abstract_excerpt":"Let $ \\mathcal{A}_1, \\ldots, \\mathcal{A}_k $ be finite sets in $ \\mathbb{Z}^n $ and let $ Y \\subset (\\mathbb{C}^*)^n $ be an algebraic variety defined by a system of equations \\[ f_1 = \\ldots = f_k = 0, \\] where $ f_1, \\ldots, f_k $ are Laurent polynomials with supports in $\\mathcal{A}_1, \\ldots, \\mathcal{A}_k$. Assuming that $ f_1, \\ldots, f_k $ are sufficiently generic, the Newton polyhedron theory computes discrete invariants of $ Y $ in terms of the Newton polyhedra of $ f_1, \\ldots, f_k $. It may appear that the generic system with fixed supports $ \\mathcal{A}_1, \\ldots, \\mathcal{A}_k $ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06392","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"}