Let be a morphism of complex manifolds, and assume that is compact. Let be a subsheaf which is closed under the Lie bracket. The present paper contains an elementary and very geometric argument to show that all obstructions to deforming along the sheaf lie in , where is the image of under the pull-back of the inclusion map. Special cases of this result include Miyaoka's theory of deformation along a foliation, Keel-McKernan's logarithmic deformation theory and deformations with fixed points.
Cite this article
Stefan Kebekus, Stavros Kousidis, Daniel Lohmann, Deformations along subsheaves. Enseign. Math. 56 (2010), no. 3/4, pp. 287–313DOI 10.4171/LEM/56-3-3