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Normal Crossings Degenerations of Symplectic Manifolds

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Abstract

We use local Hamiltonian torus actions to degenerate a symplectic manifold to a normal crossings symplectic variety in a smooth one-parameter family. This construction, motivated in part by the Gross–Siebert and B. Parker’s programs, contains a multifold version of the usual (two-fold) symplectic cut construction and in particular splits a symplectic manifold into several symplectic manifolds containing normal crossings symplectic divisors with shared irreducible components in one step.

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Author notes

  1. Mohammad Farajzadeh Tehrani

    Present address: Department of Mathematics, The University of Iowa, Iowa City, IA, 52242, USA

Authors and Affiliations

  1. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794, USA

    Mohammad Farajzadeh Tehrani

  2. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    Aleksey Zinger

Authors
  1. Mohammad Farajzadeh Tehrani
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  2. Aleksey Zinger
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Corresponding author

Correspondence to Mohammad Farajzadeh Tehrani.

Additional information

A. Zinger was partially supported by NSF Grant 1500875 and MPIM.

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Farajzadeh Tehrani, M., Zinger, A. Normal Crossings Degenerations of Symplectic Manifolds. Peking Math J 2, 275–351 (2019). https://doi.org/10.1007/s42543-019-00017-y

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  • DOI: https://doi.org/10.1007/s42543-019-00017-y

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