{"paper":{"title":"On Landau-Ginzburg systems, Quivers and Monodromy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Yochay Jerby","submitted_at":"2013-10-09T11:34:40Z","abstract_excerpt":"Let $X$ be a toric Fano manifold and denote by $Crit(f_X) \\subset (\\mathbb{C}^{\\ast})^n$ the solution scheme of the corresponding Landau-Ginzburg system of equations. For toric Del-Pezzo surfaces and various toric Fano threefolds we define a map $L : Crit(f_X) \\rightarrow Pic(X)$ such that $\\mathcal{E}_L(X) : = L(Crit(f_X)) \\subset Pic(X)$ is a full strongly exceptional collection of line bundles. We observe the existence of a natural monodromy map $$ M : \\pi_1(L(X) \\setminus R_X,f_X) \\rightarrow Aut(Crit(f_X))$$ where $L(X)$ is the space of all Laurent polynomials whose Newton polytope is equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2436","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"}