Bundle of principal parts
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.
