Is there any nontrivial example of Generalized complex groupoid?
By trivial, I mean all the classes of symplectic groupoids/ Abelian varieties as well as their products.
What I mean is that, is there any example of a groupoid in the category of generalized complex (GC) manifolds, in the sense of Hitchin. GC geometry is a way to unify complex geometry and symplectic geometry in to one realm. The definition could be found in wiki.
The space of arrows is a generalized complex manifold, and the source and target maps are generalized complex morphisms.
I can only come up with trivial examples, which are symplectic/complex, so are not real examples reflecting the nature of the theory.
-Any complex manifold is a GC manifold, so any abelian variety is a GC groupoid.
-Any symplectic manifold is a GC manifold, so any symplectic groupoid is also a GC groupoid.
-any product of these examples is also a GC groupoid.
But I can not find out any other example.