{"paper":{"title":"Symplectic structures on moduli spaces of sheaves via the Atiyah class","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Kuznetsov, D. Markushevich","submitted_at":"2007-03-09T13:40:51Z","abstract_excerpt":"Several situations are known when a holomorphic 2-form on a moduli space of sheaves over some base S is induced by a holomorphic 2-form on S. Moreover, the closedness of the 2-form on the base implies the closedness on the moduli space, which provides a stock of symplectic structures on moduli spaces (Mukai, Kobayashi, O'Grady, Tyurin, Huybrechts--Lehn). A parallel theory was developed for bivector fields and Poisson structures (Bottacin).\n  However, there exist symplectic moduli spaces of sheaves over bases that have no holomorphic forms at all. A well-known example (Beauville--Donagi) is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703264","kind":"arxiv","version":2},"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"}