{"paper":{"title":"Generating Sequences and Semigroups of Valuations on 2-Dimensional Normal Local Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arpan Dutta","submitted_at":"2018-04-12T19:46:21Z","abstract_excerpt":"In this paper we develop a method for constructing generating sequences for valuations dominating the ring of a two dimensional quotient singularity. Suppose that $K$ is an algebraically closed field of characteristic zero, $K[X,Y]$ is a polynomial ring over $K$ and $\\nu$ is a rational rank 1 valuation of the field $K(X,Y)$ which dominates $K[X,Y]_{(X,Y)}$. Given a finite Abelian group $H$ acting diagonally on $K[X,Y]$, and a generating sequence of $\\nu$ in $K[X,Y]$ whose members are eigenfunctions for the action of $H$, we compute a generating sequence for the invariant ring $K[X,Y]^H$. We us"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04704","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/1804.04704/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"}