In this paper we give a description of the first order deformation space of a regular embedding X↪Y of reduced algebraic schemes. We compare our result with results of Ran (in particular, Deformation of Maps, Algebraic Curves and Projective Geometry (Trento, 1988), 246–253, Lecture Notes in Math, vol. 1389. Springer, Berlin, 1989, Prop. 1.3).
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