Deformations along subsheaves

Details Deformations along subsheaves Deformations along subsheaves

2009-05-17

arxiv.org/abs/0905.2749v2

Mathematics

Algebraic Geometry

Removed an unnecessary projectivity assumption and implemented several smaller changes, suggested to us by the referee. To app

Scientific paper

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 H^1(Y, F_Y) of the sheaf F_Y, which is the image of f^*(F) in f^*(T_X) 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.

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