Resolution of singularities

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0, this was proved by Heisuke Hironaka in 1964; while for varieties of dimension at least 4 over fields of characteristic p, it is an open problem. == Definitions == Originally the problem of resolution of singularities was to find a nonsingular model for the function field of a variety X, in other words a complete non-singular variety X′ with the same function field.

Source: Wikipedia — Resolution of singularities (CC BY-SA 4.0)

Resolution of singularities

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0, this was proved by Heisuke Hironaka in 1964; while for varieties of dimension at least 4 over fields of characteristic p, it is an open problem. == Definitions == Originally the problem of resolution of singularities was to find a nonsingular model for the function field of a variety X, in other words a complete non-singular variety X′ with the same function field.

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Source: Wikipedia "Resolution of singularities" · CC BY-SA 4.0

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