{"paper":{"title":"Verdier specialization via weak factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Paolo Aluffi","submitted_at":"2010-09-13T19:29:58Z","abstract_excerpt":"Let X in V be a closed embedding, with V - X nonsingular. We define a constructible function on X, agreeing with Verdier's specialization of the constant function 1 when X is the zero-locus of a function on V. Our definition is given in terms of an embedded resolution of X; the independence on the choice of resolution is obtained as a consequence of the weak factorization theorem of Abramovich et al. The main property of the specialization function is a compatibility with the specialization of the Chern class of the complement V-X. With the definition adopted here, this is an easy consequence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2483","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"}