{"paper":{"title":"Supergeometry of $\\Pi$-Projective Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Simone Noja","submitted_at":"2017-06-05T14:55:32Z","abstract_excerpt":"In this paper we prove that $\\Pi$-projective spaces $\\mathbb{P}^n_\\Pi$ arise naturally in supergeometry upon considering a non-projected thickening of $\\mathbb{P}^n$ related to the cotangent sheaf $\\Omega^1_{\\mathbb{P}^n}$. In particular, we prove that for $n \\geq 2$ the $\\Pi$-projective space $\\mathbb{P}^n_\\Pi$ can be constructed as the non-projected supermanifold determined by three elements $(\\mathbb{P}^n, \\Omega^1_{\\mathbb{P}^n}, \\lambda)$, where $\\mathbb{P}^n$ is the ordinary complex projective space, $\\Omega^1_{\\mathbb{P}^n}$ is its cotangent sheaf and $\\lambda $ is a non-zero complex nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01359","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"}