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For questions about minimal surfaces in the sense of Riemannian geometry (as opposed to complex geometry).
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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 …