{"paper":{"title":"Computing resolutions of quotient singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Maria Donten-Bury, Simon Keicher","submitted_at":"2016-02-29T22:07:50Z","abstract_excerpt":"Let $G\\subseteq GL(n)$ be a finite group without pseudo-reflections. We present an algorithm to compute and verify a candidate for the Cox ring of a resolution $X\\rightarrow \\mathbb{C}^n/G$, which is based just on the geometry of the singularity $\\mathbb{C}^n/G$, without further knowledge of its resolutions. We explain the use of our implementation of the algorithms in Singular. As an application, we determine the Cox rings of resolutions $X\\rightarrow \\mathbb{C}^3/G$ for all $G\\subseteq GL(3)$ with the aforementioned property and of order $|G|\\leq 12$. We also provide examples in dimension 4."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00071","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"}