Two-dimensional Lagrangian singularities and bifurcations of gradient lines II

Motivated by mirror symmetry, we consider the Lagrangian fibration R → R and Lagrangian maps f : L →֒ R → R, 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. Supported by a JSPS Postdoctoral fellowship 2000 Mathematics Subject Classification: 37G25, 53D12, 70K60 E-Mail address: [email protected]