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":
... 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 ...
... 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 (18711922)