{"paper":{"title":"On Landau-Ginzburg Systems and $\\mathcal{D}^b(X)$ of projective bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Yochay Jerby","submitted_at":"2014-12-08T18:21:29Z","abstract_excerpt":"Let $X=\\mathbb{P}(\\mathcal{O}_{\\mathbb{P}^s} \\oplus \\bigoplus_{i=1}^r \\mathcal{O}_{\\mathbb{P}^s}(a_i))$ be a Fano projective bundle over $\\mathbb{P}^s$ and denote by $Crit(X) \\subset (\\mathbb{C}^{\\ast})^n$ the solution scheme of the Landau-Ginzburg system of equations of $X$. We describe a map $E : Crit(X) \\rightarrow Pic(X)$ whose image $\\mathcal{E}= \\{E(z) | z \\in Crit(X) \\}$ is the full strongly exceptional collection on $X$ found by Costa and Mir$\\acute{\\textrm{o}}$-Roig. We further show that $Hom(E(z),E(w))$ for $z,w \\in Crit(X)$ can be described in terms of a monodromy group acting on $C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2687","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":""},"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"}