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

the restrictions of projections

Then the bundle of n-th order principal parts is[1] Then

and there is a natural exact sequence of vector bundles[2] where

is the sheaf of differential one-forms on X.

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