Stability of Kapranov bundles on quadrics
type: Item
instance of: scholarly article
title: Stability of Kapranov bundles on quadrics
zbMATH Open document ID: 0866.14010
DOI: 10.1007/BF01759351
author: Raffaella Paoletti
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1996-07-07T00:00:00Z
review text: Let \(Q\) a smooth quadric hypersurface in \(\mathbb{P}^{n+1}\). In 1988 Kapranov introduced the vector bundles \(\psi_k\) on \(Q\) for \(0\leq k\leq n-1\) in order to construct a resolution of the diagonal in \(Q\times Q\). By using these bundles, the author gave a description of the derived category \(D^b(\text{Coh} (Q))\) and stated for quadrics a result analogous to Beilinson's theorem for projective spaces. For \(0\leq k\leq n-1\), the bundles \(\psi_k\) are simple and homogeneous but associated to a reducible representation. In this work we prove that they are conveniently suitably adapting to our case a criterion of stability for homogeneous vector bundles due to Rohmfeld. The proof consists of the analysis of the many possible homogeneous subvector bundles of the \(\psi_k\); without giving a complete description of them, we are able to bound their slope.
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J70
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 878427
zbMATH Keywords: quadric hypersurface
zbMATH Keywords: derived category
zbMATH Keywords: reducible representation
zbMATH Keywords: homogeneous subvector bundles
zbMATH Keywords: slope
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 878427