{"paper":{"title":"Bounded deformations of $(\\epsilon,\\delta)$-log canonical singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jihao Liu, Jingjun Han, Joaqu\\'in Moraga","submitted_at":"2019-03-17T23:51:44Z","abstract_excerpt":"In this paper we study $(\\epsilon,\\delta)$-lc singularites, i.e. $\\epsilon$-lc singularities admitting a $\\delta$-plt blow-up. We prove that $n$-dimensional $(\\epsilon,\\delta)$-lc singularities are bounded up to a deformation, and $2$-dimensional $(\\epsilon,\\delta)$-lc singularities form a bounded family. Furthermore, we give an example which shows that $(\\epsilon,\\delta)$-lc singularities are not bounded in higher dimensions, even in the analytic sense."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07202","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":""},"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"}