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I would like to have some references to understand simultaneous resolutions in families. I would like to know if there are some generalizations of the statement:

Let $V\rightarrow B$ be a three dimensional family of nodal surfaces (over $\mathbb{C}$). Then, there exists a two sheeted cover $B'\rightarrow B$ such that pulling back $V$ to $B'$ we get a smooth family, in which singular fibres are replaced by their smooth models.

The only reference I have for this result is Atiyah's paper http://rspa.royalsocietypublishing.org/content/247/1249/237 from 1958.

Thanks

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    $\begingroup$ If you can read french, the book Séminaire sur les Singularités des Surfaces (Springer Lecture Notes 777) is devoted to this subject -- look in particular at Pinkham's lecture. $\endgroup$
    – abx
    Commented Nov 29, 2016 at 5:10

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