# Does the support of a regular holonomic D-module always have finitely many orbits?

I am learning about $D$-module theory and came across a theorem that says that coherent equivariant $D$-modules whose support has finitely many orbits are automatically regular holonomic. Are there examples where the converse statement is false?

• D-modules make sense on spaces that have no group action, so this question doesn't make much sense. Take, for example, the $\mathcal D$-module $\mathcal O_{\mathbb A^1}$, and use the trivial group action on ${\mathbb A^1}$. – Allen Knutson Apr 27 '16 at 17:17