{"paper":{"title":"Nongeneric J-holomorphic curves in symplectic 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dusa McDuff","submitted_at":"2012-11-11T15:52:30Z","abstract_excerpt":"This note discusses the structure of J-holomorphic curves in symplectic 4-manifolds (M,\\om) when J\\in \\Jj(\\Ss), the set of \\om-tame J for which a fixed chain \\Ss of transversally intersecting embedded spheres of self-intersection \\le -2 is J-holomorphic. Extending work by Biran (in Invent. Math. (1999)), it shows that when (M,\\om) is the blow up of a rational or ruled symplectic 4-manifold, any homology class A\\in H_2(M;\\Z), with nonzero Gromov invariant and nonnegative intersection both with the spheres in \\Ss and with the exceptional classes other than A, has an embedded J-holomorphic repres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2431","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"}