{"paper":{"title":"Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.SG","authors_text":"Hsian-Hua Tseng, Kwokwai Chan, Naichung Conan Leung, Siu-Cheong Lau","submitted_at":"2012-09-27T03:37:57Z","abstract_excerpt":"Let $X$ be a compact toric K\\\"ahler manifold with $-K_X$ nef. Let $L\\subset X$ be a regular fiber of the moment map of the Hamiltonian torus action on $X$. Fukaya-Oh-Ohta-Ono defined open Gromov-Witten (GW) invariants of $X$ as virtual counts of holomorphic discs with Lagrangian boundary condition $L$. We prove a formula which equates such open GW invariants with closed GW invariants of certain $X$-bundles over $\\mathbb{P}^1$ used to construct the Seidel representations for $X$. We apply this formula and degeneration techniques to explicitly calculate all these open GW invariants. This yields "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6119","kind":"arxiv","version":4},"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"}