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

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

**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 ...

### Famous quotes containing the word resolution:

“Had I been less resolved to work, I would perhaps had made an effort to begin immediately. But since my *resolution* was formal and before twenty four hours, in the empty slots of the next day where everything fit so nicely because I was not yet there, it was better not to choose a night at which I was not well-disposed for a debut to which the following days proved, alas, no more propitious.... Unfortunately, the following day was not the exterior and vast day which I had feverishly awaited.”

—Marcel Proust (1871–1922)