{"paper":{"title":"Non Projected Calabi-Yau Supermanifolds over $\\mathbb{P}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Riccardo Re, Sergio L. Cacciatori, Simone Noja","submitted_at":"2017-06-05T14:42:55Z","abstract_excerpt":"We start a systematic study of non-projected supermanifolds, concentrating on supermanifolds with fermionic dimension 2 and with the reduced manifold a complex projective space. We show that all the non-projected supermanifolds of dimension $2|2$ over $\\mathbb{P}^2$ are completely characterised by a non-zero 1-form $\\omega$ and by a locally free sheaf $\\mathcal{F}$ of rank $0|2$, satisfying $Sym^2 \\mathcal{F} \\cong K_{\\mathbb{P}^2}$. Denoting such supermanifolds with $\\mathbb{P}^{2}_\\omega(\\mathcal{F})$, we show that all of them are Calabi-Yau supermanifolds and, when $\\omega \\neq 0$, they are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01354","kind":"arxiv","version":3},"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"}