{"paper":{"title":"A continuity theorem for families of sheaves on complex surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Andrei Teleman, Matei Toma, Nicholas Buchdahl","submitted_at":"2016-12-30T10:49:38Z","abstract_excerpt":"We prove that any flat family $(\\mathcal{ F}_u)_{u\\in U}$ of rank 2 torsion-free sheaves on a Gauduchon surface defines a continuous map on the semi-stable locus $U^{\\mathrm {ss}}:=\\{u\\in U \\ |\\ \\mathcal{ F}_u\\hbox{ is slope semi-stable}\\}$ with values in the Donaldson-Uhlenbeck compactification of the corresponding instanton moduli space. In the general (possibly non-K\\\"ahlerian) case, the Donaldson-Uhlenbeck compactification is not a complex space, and the set $U^{\\mathrm {ss}}$ can be a complicated subset of the base space $U$ that is neither open or closed in the classical topology, nor lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09451","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"}