{"paper":{"title":"The Topology of Equivariant Hilbert Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Dori Bejleri, Gjergji Zaimi","submitted_at":"2015-12-17T20:55:02Z","abstract_excerpt":"For $G$ a finite group acting linearly on $\\mathbb{A}^2$, the equivariant Hilbert scheme $\\operatorname{Hilb}^r[\\mathbb{A}^2/G]$ is a natural resolution of singularities of $\\operatorname{Sym}^r(\\mathbb{A}^2/G)$. In this paper we study the topology of $\\operatorname{Hilb}^r[\\mathbb{A}^2/G]$ for abelian $G$ and how it depends on the group $G$. We prove that the topological invariants of $\\operatorname{Hilb}^r[\\mathbb{A}^2/G]$ are periodic or quasipolynomial in the order of the group $G$ as $G$ varies over certain families of abelian subgroups of $GL_2$. This is done by using the Bialynicki-Biru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05774","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"}