{"paper":{"title":"Projective Superspaces in Practice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Sergio Luigi Cacciatori, Simone Noja","submitted_at":"2017-08-09T13:02:52Z","abstract_excerpt":"We study the supergeometry of complex projective superspaces $\\mathbb{P}^{n|m}$. First, we provide formulas for the cohomology of invertible sheaves of the form $\\mathcal{O}_{\\mathbb{P}^{n|m}} (\\ell)$, that are pull-back of ordinary invertible sheaves on the reduced variety $\\mathbb{P}^n$. Next, by studying the even Picard group $\\mbox{Pic}_0 (\\mathbb{P}^{n|m})$, classifying invertible sheaves of rank $1|0$, we show that the sheaves $\\mathcal{O}_{\\mathbb {P}^{n|m}} (\\ell)$ are not the only invertible sheaves on $\\mathbb{P}^{n|m}$, but there are also new genuinely supersymmetric invertible shea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02820","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"}