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
Famous quotes containing the word resolution:
“Some hours seem not to be occasion for any deed, but for resolves to draw breath in. We do not directly go about the execution of the purpose that thrills us, but shut our doors behind us and ramble with prepared mind, as if the half were already done. Our resolution is taking root or hold on the earth then, as seeds first send a shoot downward which is fed by their own albumen, ere they send one upward to the light.”
—Henry David Thoreau (1817–1862)