In algebraic geometry, given a line bundle L on a smooth variety X, the bundle of n-th order principal parts of L is a vector bundle of rank that, roughly, parametrizes n-th order Taylor expansions of sections of L. Precisely, let I be the ideal sheaf defining the diagonal embedding and the restrictions of projections to . Then the bundle of n-th order principal parts is Then and there is a natural exact sequence of vector bundles where is the sheaf of differential one-forms on X.