Bounding patterns for the cohomology of vector bundles

Abstract

Let t ∈ N, let K be a field and let V t K denote the class of all algebraic vector bundles over the projective space P t K . The cohomology table of a bundle E ∈ V t K is defined as the family of non-. . , t} × Z is said to be a bounding pattern for the cohomology of vector bundles over P t K if for each family (h (i,n) ) (i,n)∈S of non-negative integers, the set of cohomology tablesfor all (i, n) ∈ S} is finite. Our main result says that this is the case if and only if S contains a quasi-diagonal of width t, that is, a set of the form {(i, n i )| i = 0, . . . , t} with integers n 0 > n 1 > · · · > n t .