{"paper":{"title":"Rees algebras on smooth schemes: integral closure and higher differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Orlando Villamayor","submitted_at":"2006-06-30T17:31:42Z","abstract_excerpt":"Let $V$ be a smooth scheme over a field $k$, and let $\\{I_n, n\\geq 0\\}$ be a filtration of sheaves of ideals in $\\calo_V$, such that $I_0=\\calo_V$, and $I_s\\cdot I_t\\subset I_{s+t}$. In such case $\\bigoplus I_n$ is called a Rees algebra.\n  A Rees algebra is said to be a Diff-algebra if, for any two integers $N>n$ and any differential operator $D$ of order $n$, $D(I_N)\\subset I_{N-n}$. Any Rees algebra extends to a smallest Diff-algebra.\n  There are two ways to define extensions of Rees algebras, and both are of interest in singularity theory. One is that defined by taking integral closures (in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606795","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"}