{"paper":{"title":"Graph potentials and symplectic geometry of moduli spaces of vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.QA","math.RT","math.SG"],"primary_cat":"math.AG","authors_text":"Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay","submitted_at":"2022-06-23T09:59:24Z","abstract_excerpt":"We give the first examples of Fano manifolds with multiple optimal tori, i.e.~we construct monotone Lagrangian tori $L$, such that the weighted number of holomorphic Maslov index two discs with boundary on $L$ equals the upper bound given by the symplectic invariant $\\limsup_n ([m_0(L)^n]_{x^0})^{1/n}$, where $m_0(L)$ is the Floer potential.\n  To every trivalent graph $\\gamma$ of genus $g$ we associate an optimal torus $L_\\gamma$ on the celebrated symplectic Fano manifold $\\mathcal{N}_g$ (of complex dimension $3g-3$) with $\\mathrm{T}_{\\mathcal{N}_g} = 8g-8$), given by the character variety of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.11584","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/2206.11584/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"}