Isoperiodic foliation on the stratum of codimension one in the space of real-normalized differentials

Meromorphic differentials on Riemann surfaces are referred to as realnormalized in case all their periods are real. Moduli spaces of real-normalized differentials were first considered in the works of I.Krichever, where they were used to provide more elementary proofs for a number of theorems on the geometry of moduli spaces of curves. Moduli spaces of real-normalized differentials with prescribed sets of poles and residues at them are naturally stratified by the orders of the zeroes. In the recent work of I. Krichever, S. Lando, A. Skripchenko, the authors describe the stratum of the highest dimension in the space of real-normalized differential with a single pole of order two. In this work we make the next step, describing isoperiodic foliation in the stratum of codimension 1.