{"paper":{"title":"Galkin's Lower bound Conjecure for Lagrangian and orthogonal Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daewoong Cheong, Manwook Han","submitted_at":"2019-06-26T11:42:51Z","abstract_excerpt":"Let $M$ be a Fano manifold, and $H^\\star(M;\\mathbb{C})$ be the quantum cohomology ring of $M$ with the quantum product $\\star.$ For $\\sigma \\in H^*(M;\\mathbb{C})$, denote by $[\\sigma]$ the quantum multiplication operator $\\sigma\\star$ on $H^*(M;\\mathbb{C})$. It was conjectured several years ago \\cite{GGI, GI} and has been proved for many Fano manifols \\cite{CL1, CH2, LiMiSh, Ke}, including our cases, that the operator $[c_1(M)]$ has a real valued eigenvalue $\\delta_0$ which is maximal among eigenvaules of $[c_1(M)]$. Galkin's lower bound conjecture \\cite{Ga} states that for a Fano manifold $M,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11646","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":""},"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"}