{"paper":{"title":"Cosection localization via shifted symplectic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hyeonjun Park, Young-Hoon Kiem","submitted_at":"2025-04-28T07:47:47Z","abstract_excerpt":"The purpose of this paper is to shed a new light on classical constructions in enumerative geometry from the view point of derived algebraic geometry. We first prove that the cosection localized virtual cycle of a quasi-smooth derived Deligne-Mumford stack with a $(-1)$-shifted closed $1$-form is equal to the virtual Lagrangian cycle of the degeneracy locus which is $(-2)$-shifted symplectic. We next establish a shifted analogue of the Lagrange multipliers method which gives us the quantum Lefschetz theorems as immediate consequences of the equality of virtual cycles. Lastly we study derived a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.19542","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.19542/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"}