{"paper":{"title":"The geometry of $\\Pi$-invertible sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AG","authors_text":"Stephen Kwok","submitted_at":"2014-01-16T11:30:42Z","abstract_excerpt":"Using the fact that $\\Pi$-invertible sheaves can be interpreted as locally free sheaves of modules for the super skew field $\\mathbb{D}$, we give a new construction of the $\\Pi$-projective superspace $\\mathbb{P}^n_{\\Pi, B}$ over affine $k$ superschemes $B$, $k$ an algebraically closed field. We characterize morphisms into $\\mathbb{P}^n_{\\Pi, B}$ and give a new interpretation of the composition of $\\Pi$-invertible sheaves in terms of the algebra of $\\mathbb{D}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3991","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"}