All Questions
Tagged with resolution-of-singularities singularity-theory
61 questions
3
votes
0
answers
157
views
Resolving complete intersections of quadrics with singularities
Suppose that $X$ is a complete intersection of quadrics in $\mathbb P^n_{\mathbb C}$. Is there some straightforward procedure to resolve the singularities of $X$?
For example, can one stratify ...
- 14.3k
3
votes
1
answer
268
views
Rationality of higher dimensional du Val singularities
I am interested in the isolated singularity defined over $\mathbb{C}$ by
$$
x_1^2+\cdots + x_n^2+x_{n+1}^k=0,
$$
where $n>2$ and $k>2$.
I would like to know whether this singularity is rational,...
- 2,384
3
votes
0
answers
82
views
Singularities of fibrations 2
This question is related to my previous question:
Singularities of fibrations
Assume that $X$ is a complete intersection irreducible $3$-fold in a product of projective spaces. So that $X$ is ...
- 8,998
4
votes
2
answers
611
views
Vanishing associated to a resolution of singularities
Let $\pi: V\to W$ be a resolution of singularities, let $E \subset V$ be the exceptional divisor, and let $F$ be a coherent sheaf such that $R^i\pi_*F=0$ for $i>0$.
Can we conclude that $R^i\...
- 2,218
1
vote
0
answers
189
views
A definition of arithmetic divisor with conic singularities?
I have a question related to the preprint "Heights and metrics with logarithmic singularities" by G. Freixas i Montplet.
Let $X$ be an arithmetic variety with arithmetic divisor $D$ how can we ...
user21574
6
votes
1
answer
267
views
Are codimension one foliations of $\mathbb{R}^{n}-\{0\}$ with compact leaves, stable at origin?
Assume that we have a codimension one foliation of $\mathbb{R}^{n}-\{0\}$ with compact leaves.
Is it true to say that the foliation is stable at origin:That is: for every neighborhood $V$ of $0$,...
- 366
1
vote
0
answers
74
views
Simple question about surface singularities
Given $\epsilon \in (0,1)$, is it possible to find two finite familes $\mathcal{F}$ and $\mathcal{P}$ of weighted graphs, such that the weighted graph of the minimum resolution of any $\epsilon$-klt ...
- 1,595
2
votes
1
answer
110
views
Determining the desingularization from the complete local ring
Suppose I have a curve $C$ over a field $k$ and that $p$ is a singular point of $C$. Let $f : X \to C$ be the desingularization of $C$ at $p$. Then for each $s \in f^{-1}(p)$ we have a map of local ...
- 2,224
4
votes
1
answer
363
views
Property of singularity
Let $X$ be an algebraic variety, $S \subset X$ its singular locus, and $x \in S$. Say that $x$ is good if for any neighborhood $U$ of $x$, any top differential form $\omega$ on $U \setminus S$ and ...
- 2,649
3
votes
0
answers
272
views
References for resolutions of ordinary singular points
Let $X$ be a $n$-dimensional complex projective algebraic variety, let us suppose that $X$ has only isolated singularities.
Edit: Let us say that an ordinary $m$-ple singular point is an isolated ...
- 9,870
3
votes
1
answer
340
views
