A generalized complex structure is called stable if its defining
anticanonical section vanishes transversally, on a codimension-two submanifold.
Alternatively, it is a zero elliptic residue symplectic structure in the
elliptic tangent bundle associated to this submanifold. We develop
Gompf-Thurston symplectic techniques adapted to Lie algebroids, and use these
to construct stable generalized complex structures out of log-symplectic
structures. In particular we introduce the notion of a boundary Lefschetz
fibration for this purpose and describe how they can be obtained from genus one
Lefschetz fibrations over the disk.Comment: 35 pages, 2 figure
