19 Feb 2026, 14:00 CET. Talk by Aldo Witte.
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: It has symplectic type outside of a codimension-two embedded submanifold where it has complex type.
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 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.
If time permits we will also study the relation with toric geometry and T-duality. Joint work with Gil Cavalcanti and Ralph Klaasse.
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