{"paper":{"title":"(0,2)-Deformations and the $G$-Hilbert Scheme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Benjamin Gaines","submitted_at":"2014-04-16T15:51:33Z","abstract_excerpt":"We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\\mathbb{C}^3/Z_r$, focusing on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number of deformations for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the G-Hilbert scheme, and note that this lower bound can be found using methods from string theory. These methods lead us to a new way to construct the G-Hilbert scheme using the singlet count."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4291","kind":"arxiv","version":2},"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"}