{"paper":{"title":"Naturality of the hyperholomorphic sheaf over the cartesian square of a manifold of $K3^{[n]}$-type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eyal Markman","submitted_at":"2016-08-20T08:24:25Z","abstract_excerpt":"Let M be a 2n-dimensional smooth and compact moduli space of stable sheaves on a K3 surface S and U a universal sheaf over S x M. Over M x M there exists a natural reflexive sheaf E of rank 2n-2, namely the first relative extension sheaf of the two pullbacks of U to M x S x M. We prove that E is slope-stable with respect to every Kahler class on M. The sheaf E is known to deform to a sheaf E' over X x X, for every manifold X deformation equivalent to M, and we prove that E' is slope-stable with respect to every Kahler class on X. This triviality of the stability chamber structure combines with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05798","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"}