Sheaves and D-modules in integral geometry

Details Sheaves and D-modules in integral geometry Sheaves and D-modules in integral geometry

2004-10-05

arxiv.org/abs/math/0410070v1

in "Analysis, geometry, number theory: the mathematics of Leon Ehrenpreis", Contemp. Math., 251, Amer. Math. Soc., 2000, pp. 1

Mathematics

Algebraic Geometry

21 pages, LaTeX

Scientific paper

Integral geometry deals with those integral transforms which associate to ``functions'' on a manifold their integrals along submanifolds parameterized by another manifold. Basic problems in this context are range characterization--where systems of PDE appear--and inversion formulae. As we pointed out in a series of joint papers with Pierre Schapira, the language of sheaves and D-modules provides both a natural framework and powerful tools for the study of such problems. In particular, it provides a general adjunction formula which is a sort of archetypical theorem in integral geometry. Focusing on range characterization, we illustrate this approach with a discussion of the Radon transform, in some of its manifold manifestations.

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