Monads on projective space

Abstract

This is a little investigation into the classification of complexes of direct sums of line bundles on projective spaces. We consider complexes on projective k-space Pk : O_Pk(-1)^a --> O_Pk^b --> O_Pk(1)^c, with the first map injective and the second map surjective. This is called a monad. We classify completely when such monads exist. Furthermore, whenever it exists we show that the first map may be assumed to degenerate in expected codimension, which is b-a-c+1.