{"paper":{"title":"Toric Varieties with NC Toric Actions: NC Type IIA Geometry","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"El Hassan Saidi, Mohamed Bennai","submitted_at":"2003-12-17T10:10:08Z","abstract_excerpt":"Extending the usual $\\mathbf{C}^{\\ast r}$ actions of toric manifolds by allowing asymmetries between the various $\\mathbf{C}^{\\ast}$ factors, we build a class of non commutative (NC) toric varieties $\\mathcal{V}%_{d+1}^{(nc)}$. We construct NC complex $d$ dimension Calabi-Yau manifolds embedded in $\\mathcal{V}_{d+1}^{(nc)}$ by using the algebraic geometry method. Realizations of NC $\\mathbf{C}^{\\ast r}$ toric group are given in presence and absence of quantum symmetries and for both cases of discrete or continuous spectrums. We also derive the constraint eqs for NC Calabi-Yau backgrounds $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0312200","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"}