# Questions tagged [singularity-theory]

This tag is for questions relating to Singularity Theory. In singularity theory the general phenomenon of points and sets of singularities is studied, as part of the concept that manifolds (spaces without singularities) may acquire special, singular points by a number of routes.

292 questions
Filter by
Sorted by
Tagged with
36 views

### If the vector space dimension of $\mathbb{C}[[x,y]]/I$ over $\mathbb{C}$ is finite, then $I$ contains power of $(X,Y)$

I am trying to understand the proof which goes like this. If $\mathrm{dim}_{\mathbb{C}} \ \mathbb{C}[[x,y]]/I$ is finite, then $\mathbb{C}[[x,y]]/I$ has a finite composition series whose ...
38 views

### Connectedness of exceptional divisors

Let $X$ be a quasi-projective variety over $\mathbb{C}$. Let $I$ be an ideal sheaf supported at a closed point on $X$. Is the exceptional divisor for the blow-up of $X$ along the ideal sheaf $I$, ...
35 views

53 views

### Derivatives of a recursively and implicitly defined polynomial

I'm studying Frobenius Manifolds associated with $A_n$-type singularities and in order to prove some results about their potentials I need to calculate the following thing. Assume that $n$ is a fixed ...
10 views

### Examples of a birational map with conditions

I need of an example in the following situation. Let $X$ be an algebraic variety embedded as a closed subvariety of a nonsingular variety $M (i: X \rightarrow M )$. Let $\pi : \tilde{M} \rightarrow M$...
28 views

23 views

### sheaf and de Rham cohomology of projective lines glued to order $n$

Let $X = \mathbb{P}^1_k \cup_n \mathbb{P}^1_k$ be the union of two projective lines, glued together at a single point, where the gluing is of order $n$. I would like to compute the sheaf cohomology ...
30 views

### Calderon-Zygmund in $L^p$ with $2<p<+\infty$

Let $T$ be the following function: \begin{equation*} Tf(x)=P.V\int_{\mathbb{R}^n}\frac{\Omega(y)}{|y|^n}f(x-y)\,dy=\lim_{\varepsilon \rightarrow 0^{+}} \int_{|y|>\varepsilon} \frac{\Omega(y)}{|y|^n}...
42 views

### What is “log canonical threshold” in simple terms?

I'm currently learning some basic algebraic geometry and am interested in singularities of varieties. In reading about classifying singular points I've come across the log canonical threshold (LCT) as ...
42 views

28 views

### Classifying Singular Points as Regular/Irregular for Differential Equation

The question asks to find the singular points of the Differential Equation and to classify each of them as regular/irregular: $x(x^2+1)^2y''+y=0$ Edit: I gave it another shot and I ended up with 3 ...