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
Oscar Zariski (category Members of the United States National Academy of Sciences)
Oscar (1972), Collected papers. Vol. I: Foundations of algebraic geometry and resolution of singularities, Cambridge, Massachusetts-London: MIT Press,...
16 KB (1,393 words) - 08:52, 25 July 2024
surfaces, rational singularities were defined by (Artin 1966). Alternately, one can say that X {\displaystyle X} has rational singularities if and only if...
3 KB (387 words) - 17:30, 18 December 2022