Symplectic submanifolds in dimension 6 from hyperelliptic Lefschetz fibrations

2023/02/23 by Takahiro Oba, Oba, Takahiro
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2302.12146

openalex publication_date 2023/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (\mathbbCP³, ω_FS) of a fixed degree ≤ 3 are mutually diffeomorphic.

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