Normal crossings degenerations of symplectic manifolds

Tehrani, Mohammad Farajzadeh; Zinger, Aleksey

doi:10.1007/s42543-019-00017-y

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Normal crossings degenerations of symplectic manifolds

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Zinger, Aleksey
Max Planck Institute for Mathematics, Max Planck Society;

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

Tehrani, M. F., & Zinger, A. (2019). Normal crossings degenerations of symplectic manifolds. Peking Mathematical Journal, 2(3-4), 275-351. doi:10.1007/s42543-019-00017-y.

Cite as: https://hdl.handle.net/21.11116/0000-0007-0D74-9

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.