English

Microsupport of tempered solutions of D-Modules associated to smooth morphisms

Algebraic Geometry 2013-01-16 v4 Analysis of PDEs

Abstract

Let f:XYf:X\to Y be a smooth morphism of complex analytic manifolds and let FF be an R\mathbb{R}-constructible complex on YY. Let M\cal{M} be a coherent \shdX\shd_X-module. We prove that the microsupport of the solution complex of \shm\shm in the tempered holomorphic functions t\shhom(f1F,\shoX)t \shh \text{om} (f^{-1} F, \sho_X), is contained in the 1-characteristic variety of M\cal{M} associated to ff, and that the microsupport of the solution complex in the tempered microfunctions tμhom(f1F,\shoX)t\mu hom(f^{-1}F, \sho_X) is contained in the 1-microcharacteristic variety of the microlocalized of \shm\shm along TY×YXT^*Y\times_Y X. This applies in particular to the complex of solutions of \shm\shm in the sheaf of distributions holomorphic in the fibers of an arbitrary smooth morphism.

Cite

@article{arxiv.0808.0887,
  title  = {Microsupport of tempered solutions of D-Modules associated to smooth morphisms},
  author = {Teresa Monteiro Fernandes},
  journal= {arXiv preprint arXiv:0808.0887},
  year   = {2013}
}

Comments

Final version to appear in Houston Journal of Mathematics with a dedicatory added

R2 v1 2026-06-21T11:08:11.053Z