Explicit Hamiltonian Classification in the F₄(0) Toric Degeneration of ℂℙ²

Abstract

We give an explicit coordinate description of the Hamiltonian isotopy classes of the regular Lagrangian torus fibers of the smoothing b $\widehat{F}_4(0)$ of the F⁴(0) toric degeneration, expressed in the explicit Oakley-Usher coordinates on ℂℙ²(√2). For the wall fibers, they are not Hamiltonian isotopic to standard toric fibers, and no two distinct wall fibers are Hamiltonian isotopic. For the off-wall fibers, we find the standard toric fibers they are Hamiltonian isotopic to.

Keywords

Lagrangian torus / toric degeneration / Hamiltonian isotopy, symplectic reduction / displacement-energy germ / 53D12 / 53D20

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