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.
Read more about Resolution Of Singularities: Definitions, Resolution of Singularities of Curves, Resolution of Singularities of Surfaces, Resolution of Singularities in Higher Dimensions, Resolution For Schemes and Status of The Problem, Method of Proof in Characteristic Zero
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