Symplectic submanifolds in dimension 6 from hyperelliptic Lefschetz fibrations

We provide a closed, simply connected, symplectic 6 -manifold having infinitely many codimension 2 symplectic submanifolds. These are mutually homologous but homotopy inequivalent, and furthermore, they cannot admit complex structures. The key ingredient for the construction is hyperelliptic Lefschetz fibrations on 4 -manifolds. As a corollary, we present a similar result on symplectic submanifolds of codimension 2 in higher dimensions. In the appendix, we give a proof of the well-known fact that all symplectic submanifolds of codimension 2 in ({\mathbb{CP}}^{3}, \omega_{\mathrm{FS}}) of a fixed degree \leq 3 are mutually diffeomorphic.