Self-crossing stable generalized complex structures

Gil R. Cavalcanti; Ralph L. Klaasse; Aldo Witte

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arXiv · 2004.07559

Self-crossing stable generalized complex structures

Gil R. Cavalcanti·Ralph L. Klaasse·Aldo Witte

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Abstract

We extend the notion of (smooth) stable generalized complex structures to allow for an anticanonical section with normal self-crossing singularities. This weakening not only allows for a number of natural examples in higher dimensions but also sheds some light into the smooth case in dimension four. We show that in four dimensions there is a natural connected sum operation for these structures as well as a smoothing operation which changes a self-crossing stable generalized complex structure into a smooth stable generalized complex structure on the same manifold. This allows us to construct large families of stable generalized complex manifolds.

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Gil R. Cavalcanti, Ralph L. Klaasse, Aldo Witte. 2020-04-16. Self-crossing stable generalized complex structures. https://arxiv.org/abs/2004.07559

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