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About: Resolution of singularities     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatUnsolvedProblemsInMathematicsyago:Abstraction100002137yago:Attribute100024264yago:Condition113920835yago:Difficulty114408086yago:Problem114410605diseaseyago:State100024720 New Facet based on Instances of this Class

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0 this was proved in Hironaka (1964), while for varieties over fields of characteristic p it is an open problem in dimensions at least 4.