Modules of principal parts on the projective line

Abstract

The modules of principal parts P^k(E) of a locally free sheaf ε on a smooth scheme X is a sheaf of O_X-bimodules which is locally free as left and right O_X-module. We explicitly split the modules of principal parts P^k(O(n)) on the projective line in arbitrary characteristic, as left and right O_p1-modules. We get examples when the splitting-type as left module differs from the splitting-type as right module. We also give examples showing that the splitting-type of the principal parts changes with the characteristic of the base field.