{"paper":{"title":"Blowups and fibers of morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin, Bernd Ulrich, Claudia Polini","submitted_at":"2014-10-13T01:10:16Z","abstract_excerpt":"Our object of study is a rational map Psi from projective s-1 space to projective n-1 space defined by homogeneous forms g1,...,gn, of the same degree d, in the homogeneous coordinate ring R=k[x1,...,xs] of projective s-1 space. Our goal is to relate properties of Psi, of the homogeneous coordinate ring A=k[g1,...,gn] of the variety parametrized by Psi, and of the Rees algebra R[It], the bihomogeneous coordinate ring of the graph of Psi. For a regular map Psi, for instance, we prove that R[It] satisfies Serre's condition R_i, for some positive i, if and only if A satisfies R_{i-1} and Psi is b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3172","kind":"arxiv","version":3},"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"}