All Questions
Tagged with singularity-theory surfaces
11 questions
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Can a signed distance bound function surface be singular over a set of measure that is non-zero?
Motivation
This is a follow-up from my question here: Can an implicit surface be singular over a set of measure that is non-zero?.
I actually thought that the answer would be positive, but ...
- 2,386
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Can an implicit surface be singular over a set of measure that is non-zero?
Let $f:\mathbb{R}^3\to\mathbb{R}$ be a continuous function such that $S = f^{-1}(0) = \{p\in\mathbb{R}^3\,:\, f(p)=0\}$ is a surface. Let $f$ be continuously differentiable almost everywhere on an ...
- 2,386
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Examples of real High Milnor Du Val Quartics
I am looking for examples of specific quartic projective hypersurfaces over $\mathbb{P}^{3}$. So I am going off the fact the famous Kummer surface, under some parameters, have 16 real $A_{1}$ ...
- 384
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Contraction of loops on algebraic surfaces.
Suppose ${\Bbb C}$ be a complex number field and $S$ be a projective smooth surface over ${\Bbb C}$. We consider a finite etale Galois covering $\pi \colon T \to S$ of degree $d$. We consider the ...
- 893
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Is the desingularization of this surfaces of general type?
I have a family of deformation $\mathcal{X}\to B$ of a surface $S$. The surface has a finite number of singular point and it is normal.
There is a divisor $D\subset B$ such that the surface $\mathcal{...
- 255
2
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54
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What is the name of this type of object?
I am interested in the following type of objects (I will describe them later), but because I am very new to the subject of differential geometry, and I just have a very basic notion of the concepts, I ...
- 361
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837
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Deciding whether a point on a surface is singular
Consider $S^2 \in \mathbb{R}^2$. It is well known that it is a regular surface. We can parametrize (a patch of it) by (EDIT: this seems wrong, see comment)
$$x(u,v) = \cos u \cos v$$
$$y(u,v) = \sin ...
- 456
2
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Blowing up lines in projective space
In $\mathbb{A}^3$ we can transform the surface $x^2=y^2z$ to a smooth surface by blowing up the z-axis.
What if we want to resolve this surface everywhere in $\mathbb{P}^3$? If we take projective ...
- 21
3
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Find the metric around a trefoil singularity
Singular surfaces in $\mathbb{C}^2$ can be described by knots or links: $z_1^2-z_2^2=0$ is the Hopf link, $z_1^2-z_2^3=0$ is the trefoil, etc. I want to know how to determine the metric on the surface ...
- 2,685
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Do there exist double points on a surface in $\mathbb{P}_{\mathbb{C}}^3$ that are not rational?
The title explains it all.
I'm familiar with the du val singularities on surfaces, also apparently known as rational double points (http://en.wikipedia.org/wiki/Du_Val_singularity).
In http://...
- 5,375
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How many types of surface singularities multiplicity two exist?
All varieties are over $\mathbb{C}$.
Let $S$ be a reduced algebraic surface in $\mathbb{P}^3$ with a singular point $p$ of multiplicity two. The question is local so we reduce to $S \subset \mathbb{A}...
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