Geometric interplay between function subspaces and their rings of differential operators

Details Geometric interplay between function subspaces and their rings of differential operators Geometric interplay between function subspaces and their rings of differential operators

2004-03-24

arxiv.org/abs/math/0403409v1

Mathematics

Algebraic Geometry

36 pages, LaTeX

Scientific paper

We study, in the setting of algebraic varieties, finite-dimensional spaces of functions V that are invariant under a ring D^V of differential operators, and give conditions under which D^V acts irreducibly. We show how this problem, originally formulated in physics (Kamran-Milson-Olver), is related to the study of principal parts bundles and Weierstrass points (Laksov-Thorup), including a detailed study of Taylor expansions. Under some conditions it is possible to obtain V and D^V as global sections of a line bundle and its ring of differential operators. We show that several of the published examples of D^V are of this type, and that there are many more -- in particular arising from toric varieties.

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