All Questions
Tagged with several-complex-variables singularity-theory
7 questions
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Concerning the definition of a class of functions introduced by Nilsson
In the paper 'Some growth and ramification properties of certain integrals on algebraic manifolds' by Nilsson we find the following definitions:
My question is how does one prove the remark "It ...
- 360
2
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220
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Bishop's compactness theorem and convergence of analytic subset
Let $V_i$ be a sequence of $k$ dimensional analytic subsets in $\mathbb C^N$. Suppose that the volume of $V_i$ is uniformly bounded, then Bishop's compactness theorem says that $V_i$ will convergence ...
- 9,237
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74
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When a strictly positive log pluriharmonic function $g$ is equal to the norm of holomorphic function?
Suppose $V$ is a local analytic variety (singular). Suppose $g$ a strictly positive log pluriharmonic function on $V$, i.e. $\log g$ is pluriharmonic. I wonder when $g=|f|^2$, where $f$ is a ...
- 6,367
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Milnor Number of real and imaginary parts of holomorphic germs?
By performing some computations using the Singular software, I've noticed the following pattern: if $\mu$ is the Milnor Number of a holomorphic germ $f\in \mathcal{O}_n$ at the origin, then the Milnor ...
- 4,713
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Equations needed to define a normal complex surface singularity
This questions is highly related with this other question of mine: Irreducible surface singularity that is not a local set-theoretical complete intersection I just thought that a different look at the ...
- 1,409
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360
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Irreducible surface singularity that is not a local set-theoretical complete intersection
I have been looking for a criterion for the germ of an irreducible complex surface singularity $(X,x)$ to be a set-theoretical complete intersection.
A germ $(X,x)$ of an isolated complex singularity ...
- 1,409
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On Remmerts reduction
Let $(X,0)$ be a normal surface singularity. An let $\pi: \tilde{X} \to X$ be the minimal resolution. Now, we can apply a result of Oliveira (exploiting previous work by Laufer) and obtain a 1-...
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