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 formula_1 that, roughly, parametrizes "n"-th order Taylor expansions of sections of "L".
Precisely, let "I" be the ideal sheaf defining the diagonal embedding formula_2 and formula_3 the restrictions of projections formula_4 to formula_5. Then the bundle of "n"-th order principal parts is
Then formula_7 and there is a natural exact sequence of vector bundles
where formula_9 is the sheaf of differential one-forms on "X".