All Questions
Tagged with minimal-model-program singularity-theory
9 questions with no upvoted or accepted answers
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Singularities arising from the Minimal Model Program (an algebraic point of view)
I will start the story by the end:
Is there some characterization of (some of) the singularities arising from the Minimal Model Program (canonical, terminal, log-...) in terms of commutative algebra ?...
- 987
4
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Kuranishi family and smoothing of Calabi-Yau n-fold
Consider $X$ be a Calabi-Yau n-fold with at
most one ordinary double point singularity. Suppose $X$ is smoothable. Then it is known that the Kuranishi family of $X$ is a smoothing of $X$.
Now, ...
- 81
4
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Example of a non-algebraic singularity II
In an answer of this MO question, Frank Loray constructed an example of analytic singularity which is not algebraic. On the other hand, as I learned from one of Joël's comments in that question, ...
- 1,829
4
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Some examples where the plurigenera are nonconstant, when the fibres have worse singularities than canonical
Let start with a definition
Invariance of plurigenera: Choose $m$ large enough so that $mK_F$ has a non-zero global section for some fibre $F$. For any fibre $F$, we have $K_F = K_{X/D}~_{|F}$. So ...
user21574
2
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Finiteness of rational double point
Let $(R,\mathfrak{m
})$ be a three dimensional complete local ring over a field $k$ of arbitrary characteristic and let $f\in R$ and $R/f$ is a rational double point.
My question is as follows.
Are ...
- 328
2
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0
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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
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Discrepancy of general element of linear system
Let $X$ be a normal scheme and $|D|$ a linear system on $X$.
In "Singularity of Minimal Model Program" by Janos kollar p249, it says,
If $X$ is a variety over $\mathbb{C}$, and $E_j$ ...
- 328
1
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About the definition of cDV singularity
M. Reid defines cDV singularity as follow in his paper "CANONICAL 3-FOLDS"
A point $p\in X$ of a 3-fold is called a compound Du Val point if for some section H throgh $P$, $P\in H$ is a Du ...
- 328
0
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Log resolution and a divisor of pullback of function
Let $(X,x)$ be a three fold singularity
$m_{X,x}$ a ideal sheaf correspoinding to $x$.
$\sigma:Y_1\rightarrow X$ blow up at by $m_{X,x}$
$\phi:Y\rightarrow Y_1$ resolution of $Y_1$
Set $f:=\phi*\sigma$...
- 328