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Results tagged with singularity-theory
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user 14037
Singularities in algebraic/complex/differential geometry and analysis of ODEs/PDEs. Singular spaces, vector fields, etc.
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
1
vote
Accepted
Is it possible that $\int |f^2(z)|^{t+1}(P\bar{P})\phi(z) dz=0$ for all compactly supported ...
Edit notice: The answer is completely rewritten due to user2520938's comment. My original answer was that the linear operator $P$ depends on $t$, and we have $(1)$ as long as $P(t) = 0$. But as user25 …
- 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
2
votes
Is there a formula for the number of rational cuspidal curves in surfaces other than P^2?
Given a collection of isolated plane curve singularity type $\alpha = (\alpha_1,\ldots,\alpha_l)$, J. Li and Y.-J. Tzeng proved the existence of a polynomial $T_\alpha$ such that for any sufficiently …
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