19 Feb 2026, 14:00 CET. Talk by Aldo Witte.<\/p>\n
Abstract: The first example of a manifold which admits a generalized complex structure, but neither a complex or symplectic structure was 3CP2#\\bar{19 CP2} which was constructed by Cavalcanti and Gualtieri. This structure is a very special example of a GC structure called stable<\/i>: It has symplectic type outside of a codimension-two embedded submanifold where it has complex type.<\/p>\n
Afterwards many more examples where constructed by several authors, many of these manifolds appear as connected sums. However, none of the GC structures on these manifolds appeared via a connected sum procedure. We will remedy this by introducing the notion of a self-crossing stable<\/i> generalized complex structure: A generalisation of stable generalized complex structures which now degenerate on an immersed submanifold with transverse self-crossings. We will obtain a connected sum procedure for these structures, and a procedure which smoothens the immersed submanifold into an embedded one. In this manner we recover many of the existing examples in the literature as well as some new ones.<\/p>\n
If time permits we will also study the relation with toric geometry and T-duality. Joint work with Gil Cavalcanti and Ralph Klaasse.<\/p>\n\n\n