Annihilators of distributions associated with algebraic local cohomology of a hypersurface

Abstract

Let f be a real-valued real analytic function in several variables. We associate with each algebraic local cohomology class u with support in f = 0 a distribution (generalized function) ρ(u) in terms of the residue of with respect to λ at a negative integer. Then ρ constitutes a homomorphism of modules over the sheaf of analytic functions but not over the sheaf of differential operators in general. We compare the annihilator of ρ(u) in the ring of differential operators with that of u: we give sufficient conditions, together with examples, for each inclusion between the two annihilators.

Keywords:

• local cohomology
• generalized function
• residue
• annihilator

AMS Subject Classifications::

• Primary 32C38
• Secondary 46F10
• 14B15

Acknowledgements

This research was partly supported by JSPS Grant-in-Aid for Scientific Research (C) 21540200.