{"paper":{"title":"On Sp(n)-Instantons and the Fourier-Mukai Transform of Complex Lagrangians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Emily Autumn Windes, Jesse Madnick","submitted_at":"2024-07-08T21:41:09Z","abstract_excerpt":"The real Fourier-Mukai (RFM) transform relates calibrated graphs to so-called \"deformed instantons\" on Hermitian line bundles. We show that under the RFM transform, complex Lagrangian graphs in $R^{2n} \\times T^{2n}$ correspond to Sp($n$)-instantons over $R^{2n} \\times (T^{2n})^*$. In other words, the deformed Sp($n$)-instanton equation coincides with the usual Sp($n$)-instanton equation.\n  Motivated by this observation, we study Sp($n$)-instantons on hyperkahler manifolds $X^{4n}$, with an emphasis on conical singularities. First, when $X = C(M)$ is a hyperkahler cone, we relate Sp($n$)-insta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06412","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/2407.06412/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"}