The derived category of coherent sheaves on a quadric
type: Item
instance of: scholarly article
title: The derived category of coherent sheaves on a quadric
zbMATH Open document ID: 0607.18004
DOI: 10.1007/BF01077274
publication date: 1986-01-01T00:00:00Z
review text: Let E be a finite-dimensional complex vector space; endowed with a non- degenerate scalar product. Denote by P(E) the projective space associated to E and let \({\mathcal Q}\subseteq P(E)\) be the quadric of isotropic lines. The author states the following result: The bounded derived category of coherent sheaves over \({\mathcal Q}\) is equivalent (as a triangular category) to the homotopical category of finite complexes of sheaves over \({\mathcal Q}\), consisting of finite coproducts (direct sums) of elements of \(X_ 1\) (respectively of \(X_ 2)\). (Here \(X_ 1\) and \(X_ 2\) are suitable sets of sheaves associated to some canonical fibered spaces over \({\mathcal Q})\).
Mathematics Subject Classification ID: 18F20
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 3981405
zbMATH Keywords: quadric of isotropic lines
zbMATH Keywords: coherent sheaves
zbMATH Keywords: triangular category
zbMATH Keywords: homotopical category
zbMATH Keywords: finite complexes of sheaves
zbMATH Keywords: fibered spaces
author: Mikhail Kapranov
reviewed by: Nicolae Pop
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01077274
OpenAlex ID: W2026709285
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3981405