{"paper":{"title":"Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Dennis Borisov, Dominic Joyce","submitted_at":"2015-04-02T21:03:50Z","abstract_excerpt":"Let $({\\bf X},\\omega_{\\bf X}^*)$ be a separated, $-2$-shifted symplectic derived $\\mathbb C$-scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual dimension ${\\rm vdim}_{\\mathbb C}{\\bf X}=n\\in\\mathbb Z$, and $X_{\\rm an}$ the underlying complex analytic topological space. We prove that $X_{\\rm an}$ can be given the structure of a derived smooth manifold ${\\bf X}_{\\rm dm}$, of real virtual dimension ${\\rm vdim}_{\\mathbb R}{\\bf X}_{\\rm dm}=n$. This ${\\bf X}_{\\rm dm}$ is not canonical, but is independent of choices up to bordisms fixing the underlying topolog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00690","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"}