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Abstract: Let f : Y -> X be a morphism of complex projective manifolds, and let F be asubsheaf of the tangent bundle which is closed under the Lie bracket, but notnecessarily a foliation. This short paper contains an elementary and verygeometric argument to show that all obstructions to deforming the morphism falong the sheaf F lie in the first cohomology group H^1Y, F Y of the sheafF Y, which is the image of f^*F in f^*T X under the pull-back of theinclusion map.Special cases of this result include the theory of deformation along apossibly singular foliation, logarithmic deformation theory and deformationswith fixed points.



Author: Stefan Kebekus, Stavros Kousidis, Daniel Lohmann

Source: https://arxiv.org/







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