Consider M a locally free $\mathcal{O}_{\mathbb{C}^{n}}$module. does exist a theory of deformation for that type of object? I would like to know, which conditions has to satisfy the total space of a one (but also higher) parameter deformation of M in such way that each fiber is locally free.
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I think the theory you are looking for can be found in Th. 8.5.3, chap. 8 (p. 210) of the book by B. Fantechi et al., "FGA explained". 

