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arXiv · 2302.12146

Symplectic submanifolds in dimension $6$ from hyperelliptic Lefschetz fibrations

Takahiro Oba
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Abstract

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.

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Takahiro Oba. 2023-02-23. Symplectic submanifolds in dimension $6$ from hyperelliptic Lefschetz fibrations. https://arxiv.org/abs/2302.12146

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