{"paper":{"title":"Stability of a natural sheaf over the cartesian square of the Hilbert scheme of points on a K3 surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eyal Markman","submitted_at":"2015-06-20T01:48:55Z","abstract_excerpt":"Let S be a K3 surface and S^[n] the Hilbert scheme of length n subschemes of S. Over the cartesian square of S^[n] there exists a natural reflexive rank 2n-2 coherent sheaf E, which is locally free away from the diagonal. The fiber of E, over a pair of ideal sheaves of distinct subschemes, is the vector space of extensions of the first ideal sheaf by the second. We prove that E is slope stable if the rank of the Picard group of S is less than or equal to 19. The Chern classes of End(E) are known to be monodromy invariant. Consequently, the sheaf End(E) is polystable-hyperholomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06191","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"}