On spinor bundles
Let K be an algebraically closed field and let \(G=Gr(1,3)\) be the Klein quadric over K. The author uses Bejlinson's ideas [\textit{A. A. Bejlinson}, Funct. Anal. Appl. 12, 214-216 (1979); translation from Funkts. Anal. Prilozh. 12, No.3, 68-69 (1978; Zbl 0402.14006)] to prove that all coherent sheaves on G are built from two bundles by means of certain exact sequences. These two bundles are: the universal rank-2 sub-bundle and the universal rank-2 quotient bundle. In case the coherent sheaf is locally free, this representation leads to quite explicit formulas.
scientific article; zbMATH DE number 3924966