{"paper":{"title":"Gauge theoretical equivariant Gromov-Witten invariants and the full Seiberg-Witten invariants of ruled surfaces","license":"","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.SG","authors_text":"A. Teleman, Ch. Okonek","submitted_at":"2001-02-15T17:38:22Z","abstract_excerpt":"Let $(F,J,\\omega)$ be an almost K\\\"ahler manifold, $\\alpha$ a $J$-holomorphic action of a compact Lie group $\\hat K$ on $F$, and $K$ a closed normal subgroup of $\\hat K$ which leaves $\\omega$ invariant. We introduce gauge theoretical invariants for such triples $(F,\\alpha,K)$. The invariants are associated with moduli spaces of solutions of a certain vortex type equation on a Riemann surface.\n  We give explicite descriptions of the moduli spaces associated with the triple $(\\Hom(\\C^r,\\C^{r_0}), \\alpha_{\\rm can},U(r))$, where $\\alpha_{\\rm can}$ denotes the canonical action of $\\hat K=U(r)\\times"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0102119","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0102119/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}