{"paper":{"title":"Gromov-Witten theory of $\\mathsf{Hilb}^n(\\mathbb{C}^2)$ and Noether-Lefschetz theory of $\\mathcal{A}_g$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aitor Iribar Lopez, Hsian-Hua Tseng, Rahul Pandharipande","submitted_at":"2025-06-14T10:28:29Z","abstract_excerpt":"We calculate the genus 1 Gromov-Witten theory of the Hilbert scheme $\\mathsf{Hilb}^n(\\mathbb{C}^2)$ of points in the plane. The fundamental 1-point invariant (with a divisor insertion) is calculated using a correspondence with the families local curve Gromov-Witten theory over the moduli space $\\overline{\\mathcal{M}}_{1,1}$. The answer exactly matches a parallel calculation related to the Noether-Lefschetz geometry of the moduli space $\\mathcal{A}_g$ of principally polarized abelian varieties. As a consequence, we prove that the associated cycle classes satisfy a homomorphism property for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12438","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/2506.12438/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"}