Resolution of Singularities

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 WV. 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

Other articles related to "resolution of singularities, singularities":

Excellent Ring - Resolution of Singularities
... Quasi-excellent rings are closely related to the problem of resolution of singularities, and this seems to have been Grothendieck's motivation for defining them ... observed that if it is possible to resolve singularities of all complete integral local Noetherian rings, then it is possible to resolve the singularities of all reduced quasi-excellent rings. 0, which implies his theorem that all singularities of excellent schemes over a field of characteristic 0 can be resolved ...
Resolution Of Singularities - Examples - Singularities of Toric Varieties
... Singularities of toric varieties give examples of high dimensional singularities that are easy to resolve explicitly ... The singularities can be resolved by subdividing each cone into a union of cones each of which is generated by a basis for the lattice, and taking the corresponding toric variety ...

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