The derived category of coherent sheaves on a quadric
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 \({\mathcal Q})\).
scientific article; zbMATH DE number 3981405