sentences:  For 3-folds the resolution of singularities was proved in characteristic 0 by .He first proved a theorem about local uniformization of valuation rings, valid for varieties of any dimension over any field of characteristic 0.He then showed that the Zariski–Riemann space of valuations is quasi-compact (for any variety of any dimension over any field), implying that there is a finite family of models of any projective variety such that any valuation has a smooth center over at least one of these models.