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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.2436","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-10-09T11:34:40Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"23e6dbfbc56aef98124c24c140bbd655fd2d6f6fa9fb5ad8e0931ea1f34508ee","abstract_canon_sha256":"204a84d29cf43c32b42c72bb8096be34a8d31b3a67165d8867fd5f1e539a3776"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:01.026059Z","signature_b64":"blNQ4RyoU177D48/eXDHAoaYa0hlr6WN7l4aGTNtbe/IOcOTzzQCcX4y31ezmKLK9Muobfibatpn5u/36okTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ad723eff117a18a88343b05c2395ff91084711576a47db87d9c1e8e097b13ae","last_reissued_at":"2026-05-18T02:48:01.025524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:01.025524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.2436","created_at":"2026-05-18T02:48:01.025604+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2436v4","created_at":"2026-05-18T02:48:01.025604+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2436","created_at":"2026-05-18T02:48:01.025604+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLLSH37RC6QY","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLLSH37RC6QYVCBU","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLLSH37R","created_at":"2026-05-18T12:27:51.066281+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E","json":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E.json","graph_json":"https://pith.science/api/pith-number/LLLSH37RC6QYVCBUHMC4EOK77E/graph.json","events_json":"https://pith.science/api/pith-number/LLLSH37RC6QYVCBUHMC4EOK77E/events.json","paper":"https://pith.science/paper/LLLSH37R"},"agent_actions":{"view_html":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E","download_json":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E.json","view_paper":"https://pith.science/paper/LLLSH37R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2436&json=true","fetch_graph":"https://pith.science/api/pith-number/LLLSH37RC6QYVCBUHMC4EOK77E/graph.json","fetch_events":"https://pith.science/api/pith-number/LLLSH37RC6QYVCBUHMC4EOK77E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E/action/storage_attestation","attest_author":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E/action/author_attestation","sign_citation":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E/action/citation_signature","submit_replication":"https://pith.science/pith/LLLSH37RC6QYVCBUHMC4EOK77E/action/replication_record"}},"created_at":"2026-05-18T02:48:01.025604+00:00","updated_at":"2026-05-18T02:48:01.025604+00:00"}