{"paper":{"title":"Local contributions to Donaldson-Thomas invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea T. Ricolfi","submitted_at":"2016-10-26T16:30:54Z","abstract_excerpt":"Let $C$ be a smooth curve embedded in a smooth quasi-projective threefold $Y$, and let $Q^n_C=\\textrm{Quot}_n(\\mathscr I_C)$ be the Quot scheme of length $n$ quotients of its ideal sheaf. We show the identity $\\tilde\\chi(Q^n_C)=(-1)^n\\chi(Q^n_C)$, where $\\tilde\\chi$ is the Behrend weighted Euler characteristic. When $Y$ is a projective Calabi-Yau threefold, this shows that the DT contribution of a smooth rigid curve is the signed Euler characteristic of the moduli space. This can be rephrased as a DT/PT wall-crossing type formula, which can be formulated for arbitrary smooth curves. In general"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08403","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"}