Two-dimensional Lagrangian singularities and bifurcations of gradient lines II

Motivated by mirror symmetry, we consider the Lagrangian fibration R4→R2 and Lagrangian maps f:L↪R4→R2, exhibiting an unstable singularity, and study how the bifurcation locus of gradient lines, the integral curves of ∇fx, for x∈B, where fx(y)=f(y)−x⋅y, changes when f is slightly perturbed. We consider the cases when f is the germ of a fold, of a cusp and, particularly, of an elliptic umbilic.