{"paper":{"title":"Bifurcation sets and global monodromies of Newton non-degenerate polynomials on algebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Phu Phat Pham, Tat Thang Nguyen, Tien-Son Pham","submitted_at":"2018-03-26T15:20:45Z","abstract_excerpt":"Let $S\\subset \\mathbb{C}^n$ be a non-singular algebraic set and $f \\colon \\mathbb{C}^n \\to \\mathbb{C}$ be a polynomial function. It is well-known that the restriction $f|_S \\colon S \\to \\mathbb{C}$ of $f$ on $S$ is a locally trivial fibration outside a finite set $B(f|_S) \\subset \\mathbb{C}.$ In this paper, we give an explicit description of a finite set $T_\\infty(f|_S) \\subset \\mathbb{C}$ such that $B(f|_S) \\subset K_0(f|_S) \\cup T_\\infty(f|_S),$ where $K_0(f|_S)$ denotes the set of critical values of the $f|_S.$ Furthermore, $T_\\infty(f|_S)$ is contained in the set of critical values of cert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09654","kind":"arxiv","version":1},"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"}