Some Applications of Beilinson's Theorem to Projective Spaces and Quadrics

Abstract

In this paper we apply the Beilinson theorem [Functional Anal. Appl. 12 (1978), 214–216] to the following problems. (1) We give sufficient cohomological conditions in order that a coherent sheaf on Pnor on the quadric contains as direct summand a generator of the derived category (i. e. the line bundles, the bundles ofp-forms on P”, the spinor bundles and the bundles Ψi introduced by Kapranov [Inv. Math. 92 (1988), 479–508]. (2) We characterize the indecomposable sheaves of order one (with respect to H1 and H2) on P3and we show that also the diameter is one. (3) We give a new proof of the key theorem which Chang uses to characterize the arithmetically Buchsbaum subschemes of codimension 2 in Pn.