PRINCIPAL PARTS OF LINE BUNDLES ON TORIC VARIETIES

The main tool for studying the inflections (or Weierstrass points) of a mapping of a smooth projective variety into projective space are the principal parts of line bundles. In recent work by D. Cox, [2], homog eneous coordinates on a toric variety have been introduced, and in sub sequent work with V. Batyrev, [1], an Euler sequence is defined. The h omogeneous coordinates and the Euler sequence are direct generalizatio ns of the usual notions in the case of projective space. The purpose o f this note is to use the Euler sequence to describe the principal par ts of line bundles on a toric variety (Theorem 1.2). The essential ide a is to compare derivatives with respect to local and global coordinat es. Even for the case of projective space, the complete description is apparently not to be found in the literature.