{"paper":{"title":"Spectral pairs, Alexander modules, and boundary manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Laurentiu Maxim, Yongqiang Liu","submitted_at":"2016-07-19T11:15:37Z","abstract_excerpt":"Let $f: \\CN \\rightarrow \\C $ be a reduced polynomial map, with $D=f^{-1}(0)$, $\\U=\\CN \\setminus D$ and boundary manifold $M=\\partial \\U$. Assume that $f$ is transversal at infinity and $D$ has only isolated singularities. Then the only interesting non-trivial Alexander modules of $\\U$ and resp. $M$ appear in the middle degree $n$. We revisit the mixed Hodge structures on these Alexander modules and study their associated spectral pairs (or equivariant mixed Hodge numbers). We obtain upper bounds for the spectral pairs of the $n$-th Alexander module of $\\U$, which can be viewed as a Hodge-theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05521","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"}