Self-crossing stable generalized complex structures

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

Research output: Contribution to journalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)761-811
Number of pages51
JournalJournal of Symplectic Geometry
Issue number4
Publication statusPublished - 2022


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