{"paper":{"title":"Moduli Spaces of Stable Pairs in Donaldson-Thomas Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Malte Wandel","submitted_at":"2010-11-15T10:00:40Z","abstract_excerpt":"Let $(X,\\mathcal{O}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\\mathcal{D}\\in \\mathrm{coh}(X)$ and a nonnegative rational polynomial $\\delta$. Using GIT we contruct a coarse moduli space for $\\delta$-semistable pairs $(\\mathcal{E},\\phi)$ consisting of a coherent sheaf $\\mathcal{E}$ and a homomorphism $\\phi\\colon \\mathcal{D}\\rightarrow \\mathcal{E}$. We prove a chamber structure result and establish a connection to the moduli space of coherent systems constructed by Le Potier in \\cite{LeP} and \\cite{LeP2}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3328","kind":"arxiv","version":3},"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"}