2009/05/17 by Stefan Kebekus, Kebekus, Stefan, Stavros Kousidis +3
Mathematics · #13D10 #14D15 #32G10 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.AG #math.CV #math.DG #msc:13D10 #msc:14D15 #msc:32G10
paper · pdf · doi:10.48550/arxiv.0905.2749
Removed an unnecessary projectivity assumption and implemented several smaller changes, suggested to us by the referee. To appear in L'Enseignement Mathematique.
arxiv created 2010/03/29 · arxiv updated 2010/03/30
Let f : Y -> X be a morphism of complex projective manifolds, and let F be a subsheaf of the tangent bundle which is closed under the Lie bracket, but not necessarily a foliation. This short paper contains an elementary and very geometric argument to show that all obstructions to deforming the morphism f along the sheaf F lie in the first cohomology group H1(Y, FY) of the sheaf FY, which is the image of f^*(F) in f^*(TX) under the pull-back of the inclusion map. Special cases of this result include the theory of deformation along a (possibly singular) foliation, logarithmic deformation theory and deformations with fixed points.