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edited Mar 13, 2015 at 17:58

For isolated singularities, the answer is no.

In fact, it follows by resultsa result of Artin and ElkiesElkik that any deformation of an isolated singularity is algebraizable. See

Unfortunately now I have to goR. Elkik, I will give precise references laterSolutions d'équations à coefficients dans un anneau hensélien, Ann. Sci. Ecole Norm. Sup. 6 (1973), 553-603,

in particular Part IV.

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created Mar 13, 2015 at 15:59

For isolated singularities, the answer is no.

In fact, it follows by results of Artin and Elkies that any deformation of an isolated singularity is algebraizable.

Unfortunately now I have to go, I will give precise references later.