{"paper":{"title":"Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ch. Okonek, M. Duerr","submitted_at":"2004-08-10T11:42:23Z","abstract_excerpt":"In [DKO] we constructed virtual fundamental classes $[[ Hilb^m_V ]]$ for Hilbert schemes of divisors of topological type m on a surface V, and used these classes to define the Poincare invariant of V:\n  (P^+_V,P^-_V): H^2(V,Z) --> \\Lambda^* H^1(V,Z) x \\Lambda^* H^1(V,Z)\n We conjecture that this invariant coincides with the full Seiberg-Witten invariant computed with respect to the canonical orientation data.\n  In this note we prove that the existence of an integral curve $C \\subset V$ induces relations between some of these virtual fundamental classes $[[Hilb^m_V ]]$. The corresponding relatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408130","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"}