Serre duality on complex supermanifolds
type: Item
instance of: scholarly article
title: Serre duality on complex supermanifolds
zbMATH Open document ID: 0628.32012
DOI: 10.1215/S0012-7094-87-05421-4
author: Carl Haske
author: Raymond O. jun. Wells
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Let \({\mathcal F}\) be a locally free \({\mathcal O}\)-module on a compact complex supermanifold M of dimension (m\(| n)\), and let \({\mathcal B}er_{{\mathcal O}}\) be the Berezinian sheaf on M. It is proved that the duality exists between \(H^ q(M,{\mathcal F})\) and \(H^{m-q}(M,{\mathcal B}er_{{\mathcal O}}\otimes {\mathcal F}^*)\) (this is the precise analogue of Serre's original duality theorem). The proof is in the spirit of Serre's original proof, and it uses the natural duality between smooth functions and distributions.
Mathematics Subject Classification ID: 32C37
Mathematics Subject Classification ID: 32C25
zbMATH DE Number: 4021575
zbMATH Keywords: Serre duality
zbMATH Keywords: compact complex supermanifold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4021575