{"paper":{"title":"The signature of the Seiberg-Witten surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.DG","authors_text":"Andreas Malmendier","submitted_at":"2008-02-11T05:59:05Z","abstract_excerpt":"The Seiberg-Witten family of elliptic curves defines a Jacobian rational elliptic surface $\\Z$ over $\\mathbb{C}\\mathrm{P}^1$. We show that for the $\\bar{\\partial}$-operator along the fiber the logarithm of the regularized determinant $-1/2 \\log \\det' (\\bar\\partial^* \\bar\\partial)$ satisfies the anomaly equation of the one-loop topological string amplitude derived in Kodaira-Spencer theory. We also show that not only the determinant line bundle with the Quillen metric but also the $\\bar{\\partial}$-operator itself extends across the nodal fibers of $\\mathrm{Z}$. The extension introduces current "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.1363","kind":"arxiv","version":5},"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"}