{"paper":{"title":"The 2-Factoriality of the O'Grady Moduli Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arvid Perego","submitted_at":"2009-03-18T17:55:56Z","abstract_excerpt":"The aim of this work is to show that the moduli space $M_{10}$ introduced by O'Grady in \\cite{OG1} is a $2-$factorial variety. Namely, $M_{10}$ is the moduli space of semistable sheaves with Mukai vector $v:=(2,0,-2)\\in H^{ev}(X,\\mathbb{Z})$ on a projective K3 surface $X$. As a corollary to our construction, we show that the Donaldson morphism gives a Hodge isometry between $v^{\\perp}$ (sublattice of the Mukai lattice of $X$) and its image in $H^{2} (\\widetilde{M}_{10},\\mathbb{Z})$, lattice with respect to the Beauville form of the $10-$dimensional irreducible symplectic manifold $\\widetilde{M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3211","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"}