All Questions
Tagged with singularity-theory birational-geometry
10 questions with no upvoted or accepted answers
7
votes
0
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277
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Is every normalization a blowup?
I asked this at math.stackexchange, but received no reply.
Is the normalization of a variety always a blowup along some coherent ideal sheaf? If not, I would like to see a concrete counter-example.
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3
votes
0
answers
171
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Blowing-up a non reduced fiber
Let $X\rightarrow \mathbb{P}^2$ be a smooth conic bundle with a non reduced fiber $F$, and $\widetilde{X}$ the blow-up of $X$ along $F$ with exceptional divisor $F\times\mathbb{P}^1$.
I expect $\...
- 8,998
3
votes
0
answers
150
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How to distinguish the singularities on moduli space?
Let me start with concrete examples. Let $X$ be a smooth special Gushel-Mukai threefold and $\mathcal{C}(X)$ be its honest Fano surface of conics, it has two irreducible components $\mathcal{C}(X)=\...
- 1,982
3
votes
0
answers
199
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Divisorial contractions and singularities
I have a smooth $6$-fold $X\subset\mathbb{P}^n$ and a divisor $D\subset X$ cut out by a quadratic polynomial. I know that $D$ in singular along a smooth $3$-fold $Y\subset X$, and that if $Z$ is the ...
user125056
3
votes
0
answers
452
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Singularities of rational quartic surfaces
Let $X\subset \mathbb{P}^3$ be an irreducible quartic surface, defined over an algebraically closed field $k$. Suppose that $X$ is rational (i.e. birational to $\mathbb{P}^2$). Is is true that $X$ has ...
- 7,722
3
votes
0
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82
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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
2
votes
0
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137
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Discrepancy of a divisor over a different model
I also asked this question on MathStackExchange but receive no answers.
I'm reading Koll'ar and Mori's book about singularity theory. They state the following lemma without proof:
Lemma 2.30. Let $f:...
- 361
2
votes
0
answers
221
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Confusion with terminology: Crepant resolution of terminal singularities
In Theorem 1.1 of this article, Bridgeland proves derived equivalence between Crepant resolution of threefold terminal singularities. I am a little confused with this terminology. In particular, a $\...
- 2,032
2
votes
0
answers
674
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Small contractions as blow ups
To improve my chances of getting answers/ comments I post my mathstackexchange question https://math.stackexchange.com/q/2808852/42548 also here.
I am trying to learn a bit about birational morphisms:...
- 121
0
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0
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105
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Every locally free sheaf is Cohen-Macaulay on complex variety with at canonical singualities?
Suppose $X$ is a normal complex space with at most singularities, can we say any locally free sheaf on it is Cohen-Macauly?
Recall that a coherent sheaf $\mathcal{F}$ over $X$ is called (maximal) ...
- 295