{"paper":{"title":"Rigid HYM Connections on Tautological Bundles over ALE Crepant Resolutions in Dimension Three","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Anda Degeratu, Thomas Walpuski","submitted_at":"2012-07-30T13:49:45Z","abstract_excerpt":"For $G$ a finite subgroup of ${\\rm SL}(3,{\\mathbb C})$ acting freely on ${\\mathbb C}^3{\\setminus} \\{0\\}$ a crepant resolution of the Calabi-Yau orbifold ${\\mathbb C}^3\\!/G$ always exists and has the geometry of an ALE non-compact manifold. We show that the tautological bundles on these crepant resolutions admit rigid Hermitian-Yang-Mills connections. For this we use analytical information extracted from the derived category McKay correspondence of Bridgeland, King, and Reid [J. Amer. Math. Soc. 14 (2001), 535-554]. As a consequence we rederive multiplicative cohomological identities on the cre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6938","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"}