{"paper":{"title":"Finite morphisms and simultaneous reduction of the multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Ana Bravo, Carlos Abad, Orlando E. Villamayor","submitted_at":"2017-10-04T21:00:39Z","abstract_excerpt":"Let $X$ be a singular algebraic variety defined over a field $k$, with quotient field $K(X)$. Let $s \\geq 2$ be the highest multiplicity of $X$ and $F_s(X)$ the set of points of multiplicity $s$. If $Y\\subset F_s(X)$ is a regular center and $X\\leftarrow X_1$ is the blow up at $Y$, then the highest multiplicity of $X_1$ is less than or equal to $s$. A sequence of blow ups at regular centers $Y_i \\subset F_s(X_i)$, say $X \\leftarrow X_1 \\leftarrow \\dotsb \\leftarrow X_n$, is said to be a {\\em simplification} of the multiplicity if the maximum multiplicity of $X_n$ is strictly lower than that of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01805","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"}