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Self-crossing stable generalized complex structures

par Cavalcanti, Gil Ramos;Klaasse, Ralph ;Witte, Aldo
Référence Journal of symplectic geometry, 20, 4, page (761-811)
Publication Publié, 2022

Article révisé par les pairs

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Résumé :

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: in this dimension there is a natural connected sum construction 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.