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We apply the general construction developed in references [4,5] to the firstnon-trivial case of Gr^{TP}(2,4). In particular, we construct finite-gap KP-IIreal quasiperiodic solutions in the form of soliton lattice corresponding to asmooth genus 4 M-curve, which is a desingularization of a reducible rationalM-curve for soliton data in Gr^{TP}(2,4).

Real soliton lattices of KP-II and desingularization of spectral curves: the Gr^{TP}(2,4) case