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Results tagged with minimal-model-program
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user 14037
minimal model program is part of the birational classification of algebraic varieties.
1
vote
Blow up of terminal singularity and canonical singularity
The origin of the hypersurface defined by
$$x_0^2 + x_1^4 + x_2^4 + \cdots + x_n^4 = 0$$
is a canonical singularity for $n = 3$, and a terminal singularity for $n \ge 4$ (see e.g. Theorem 2 in this pa …
- 1,829
4
votes
0
answers
216
views
Example of a non-algebraic singularity II
In an answer of this MO question, Frank Loray constructed an example of analytic singularity which is not algebraic. On the other hand, as I learned from one of Joël's comments in that question, Arti …
- 1,829
1
vote
Castelnuovo and Artin contractibility criteria for families
For complex manifolds, simultaneous contractions in a family has been studied by Riemenschneider in the paper "Deformations of Rational Singularities and their Resolutions". Theorem 1 in that article …
- 1,829
2
votes
1
answer
3k
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Trivial canonical bundle
Let $X$ be a complex compact Kähler minimal surface with zero algebraic dimension and $H^2(X,\mathcal{O}_X) \ne 0$. We know that according to Enriques–Kodaira classification, $X$ is either a torus or …
- 6,871