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...
42 KB (5,453 words) - 17:04, 6 May 2024
Toric variety (section Resolution of singularities)
its cones of maximal dimension are generated by a basis of the lattice. This implies that every toric variety has a resolution of singularities given by...
9 KB (1,310 words) - 21:21, 12 June 2024
acquire singular points on the hyperplane at infinity, when its closure in projective space is taken. Resolution says that such singularities can be handled...
10 KB (1,225 words) - 09:17, 9 January 2024
Rational mapping (section Resolution of singularities)
One of the canonical examples of a birational map is the Resolution of singularities. Over a field of characteristic 0, every singular variety X...
8 KB (1,480 words) - 00:40, 28 August 2024
Excellent ring (section Resolution of singularities)
problem of resolution of singularities can be solved; Hironaka (1964) showed this in characteristic 0, but the positive characteristic case is (as of 2024)...
11 KB (1,468 words) - 01:08, 5 August 2024
Heisuke Hironaka (category Members of the French Academy of Sciences)
discussed cutting-edge research developments including the resolution of singularities problem for which Hironaka later received the Fields Medal. Hironaka...
17 KB (1,506 words) - 00:49, 27 August 2024
Standard resolution, the bar construction of resolutions in homological algebra Resolution of singularities in algebraic geometry Resolution (audio),...
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convenient setting. Much deeper is Hironaka's 1964 theorem on resolution of singularities: over a field of characteristic 0 (such as the complex numbers), every...
20 KB (2,684 words) - 22:32, 2 January 2024
Blowing up (redirect from Blow-up of a subvariety)
important way of constructing new spaces. For instance, most procedures for resolution of singularities proceed by blowing up singularities until they become...
22 KB (3,816 words) - 05:40, 26 June 2024
Normal scheme (redirect from Normalization of an algebraic variety)
singularities. Normalization is not usually used for resolution of singularities for schemes of higher dimension. To define the normalization, first suppose...
7 KB (1,087 words) - 19:07, 14 June 2024