Resurgence and Hironaka decomposition

Determine how much of the global information reconstructed by resurgence is already encoded in the Hironaka decomposition of a finite-N invariant ring.

Background

The Hironaka decomposition organizes global algebraic information about the finite-N invariant ring into primary and secondary invariants. Resurgence, by contrast, reconstructs global analytic information from perturbative data obtained locally around a saddle. The paper explicitly asks whether the algebraic information in the Hironaka decomposition already contains some or all of the global information that resurgence recovers.