{"paper":{"title":"Filtrations associated with singularities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Andr\\'as N\\'emethi, Willem Veys","submitted_at":"2024-05-17T16:36:45Z","abstract_excerpt":"We fix a complex analytic normal singularity germ $(X,o)$ of dimension $\\geq 2$ and a (not necessarily irreducible) reduced Weil divisor $(S,o)\\subset (X,o)$. The embedded resolution of the pair determines a multi-index filtration of the local ring $\\mathcal{O}_{X,o}$, which measures the embedded geometry of the pair. Furthermore, from the (induced) resolution of $(S,o)$ we also consider a multi-index filtration associated with $(S,o)$. This latter one can be lifted to a filtration of $\\mathcal{O}_{X,o}$ too. The main result proves that the second filtration of $\\mathcal{O}_{X,o}$ can be reali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.10898","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.10898/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}