An algebraic study of parametric Stokes phenomena

We investigate geometric aspects of co-equational parametric resurgence, by studying physical problems whose formal asymptotic solutions give rise to Borel transforms lying on an algebraic curve. This perspective allows us to elucidate concepts unique to parametric resurgence such as singularity structures, (virtual) turning points and the higher-order Stokes phenomenon. We construct examples as solutions to Borel plane partial differential equations using an algebraic curve ansatz before turning to the general analytic structure of co-equational resurgence problems, where we provide a systematic description of analytic continuation and Stokes constants through a Borel plane inner-outer matching procedure.