L’anneau log canonique d’une paire plt projective de dimension Kodaira deux est finement engendré.

We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension ≥ 4, over which every extension of line bundles splits.

In this paper we consider the notion of the Weyl filtration dimension and good filtration dimension of modules for a linear algebraic group. These concepts were first introduced by Friedlander and Parshall [15] and may be considered a variation of the notion of projective dimension and injective dimension respectively. (The precise definition is given in 2.2.) The Weyl filtration dimension of a...