Two-dimensional Lagrangian singularities and bifurcations of gradient lines I

Details Two-dimensional Lagrangian singularities and bifurcations of gradient lines I Two-dimensional Lagrangian singularities and bifurcations of gradient lines I

2007-03-30

arxiv.org/abs/math/0703915v1

J. Geo. Phys. 56/9 (2006), 1688-1708

Mathematics

Dynamical Systems

29 pages

Scientific paper

Motivated by mirror symmetry, we consider a Lagrangian fibration $X\to B$ and Lagrangian maps $f:L\hookrightarrow X\to B$, when $L$ has dimension 2, exhibiting an unstable singularity, and study how their caustic changes, in a neighbourhood of the unstable singularity, when slightly perturbed. The integral curves of $\nabla f_x$, for $x\in B$, where $f_x(y)=f(y)-x\cdot y$, called ``gradient lines'', are then introduced, and a study of them, in order to analyse their bifurcation locus, is carried out.

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