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arXiv · 1703.03798

Fibrations and stable generalized complex structures

Gil R. Cavalcanti·Ralph L. Klaasse
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Abstract

A generalized complex structure is called stable if its defining anticanonical section vanishes transversally, on a codimension-two submanifold. Alternatively, it is a zero elliptic residue symplectic structure in the elliptic tangent bundle associated to this submanifold. We develop Gompf-Thurston symplectic techniques adapted to Lie algebroids, and use these to construct stable generalized complex structures out of log-symplectic structures. In particular we introduce the notion of a boundary Lefschetz fibration for this purpose and describe how they can be obtained from genus one Lefschetz fibrations over the disk.

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Gil R. Cavalcanti, Ralph L. Klaasse. 2017-03-10. Fibrations and stable generalized complex structures. https://doi.org/10.1112/plms.12199

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