This talk will focus on stable generalized complex structures whose anticanonical divisor has transverse self crossings. These structures are intimately related to symplectic structures on the elliptic tangent bundle. Using this point of view we show that in four real dimensions

1) one can always smooth out a self crossing to obtain a structure with smooth anticanonical divisor,

2) for specific structrures, one can perform connected sums in a way compatible with the underlying symplectic structures.

Further, in the presence of a fibration structure,

3) “smoothing out of a self crossing” corresponds to a version of nodal trades from semi-toric geometry,

4) the connected sum of elliptic symplectic structures can also be performed in a fibration preserving manner,

And finally we show that if a 4-manifold admits an appropriate type of Lefschetz fibration and the fibers are homologically essential, then the manifold admits a stable generalized complex structure.

I will provide several examples illustrating the results above. Possibly surprising, different structures on the 4-sphere provide a fundamental piece of the puzzle.