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Characterizing the rigidity of morphisms of smooth varieties
The space $H^{0}(X,f_{0}^{*}T_{Y})$ is the tangent space at $f_0$ to the variety $\mathrm{Hom}(X,Y)$, see J. Kollár, Rational curves on algebraic varieties. Thus if it is zero, $f_0$ is an isolated po …