All Questions
Tagged with resolution-of-singularities singularity-theory
61 questions
7
votes
1
answer
762
views
Bertini's Theorem
Let $p_1,...,p_n\in\mathbb{P}^{N}$ be general points. Consider the linear system $|L|$ of hypersurfaces of degree $d$ in $\mathbb{P}^{N}$ with prescribed multiplicities $m_1,...,m_n$ at $p_1,...,p_n$. ...
- 66.3k
8
votes
3
answers
918
views
Contracting a rational curve in a Calabi-Yau threefold
Let $X$ be a Calabi-Yau threefold and $C \subset X$ be a rational curve with $N_{C/X}\cong \mathcal{O}\oplus \mathcal{O}(-2)$. Can one contract the curve $C$? Assuming the answer is yes, what kind of ...
CommunityBot
- 1
4
votes
2
answers
1k
views
Varieties with big anti-canonical divisor
I recently heard about the following problem:
Let $X$ be a projective variety with klt singularities and such that $-K_X$ is big. Is $X$ a Mori Dream Space ?
Now, $-K_X$ big if and only if $-K_X -\...
- 8,998
3
votes
2
answers
513
views
Which isolated surface singularity comes from a -5 curve?
Define the surface $X$ to be the total space of $\mathcal{O}_{\mathbb{P}^1}(-5)$.
By contracting the exceptional curve in $X$, we get a surface with an isolated singularity. I am looking for the ...
- 8,998
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 ...
- 38k
3
votes
3
answers
392
views
Contractibility of curves and embedding into projective space
Let $f:X \to Y$ be a proper surjective morphism of projective surfaces such that there exists a curve $C \subset X$ for which $f|_{X\backslash C}$ is an isomorphism and $f(C)$ is a set of points. ...
- 42.9k
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
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\...
- 42.9k
10
votes
2
answers
1k
views
Resolution of singularities for flat families.
Is there a resolution of singularities for flat families?
More precisely, if $X \rightarrow \mathbb{A} ^n$ is a flat map, does there exist a map $Y \rightarrow X$ such that, for every $p \in \mathbb{...
- 42.9k
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 ...
- 20.5k