Toric degeneration and non-displaceable Lagrangian tori in $S^2 \times S^2$

Abstract

In this article, using the idea of toric degeneration and the computation of the full potential function of Hirzebruch surface $F_2$, which is \emph{not} Fano, we produce a continuum of Lagrangian tori in $S^2 \times S^2$ which are non-displaceable under the Hamiltonian isotopy.