Journal of Symplectic Geometry

Volume 20 (2022)

Number 4

Self-crossing stable generalized complex structures

Pages: 761 – 811



Gil R. Cavalcanti (Department of Mathematics, Utrecht University, Utrecht, The Netherlands)

Ralph L. Klaasse (Département de Mathématique, Université libre de Bruxelles, Belgium)

Aldo Witte (Department of Mathematics, Utrecht University, Utrecht, The Netherlands)


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.

Received 2 August 2021

Accepted 19 October 2021

Published 16 March 2023