All Questions
8 questions with no upvoted or accepted answers
5
votes
0
answers
165
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Do quasi-excellent rings have a good constructive definition?
$\DeclareMathOperator\Sh{Sh}$Informally, a quasi-excellent ring is a Noetherian ring with a few technical extra regularity conditions that make it turns out to be the largest class of rings that allow ...
- 1,947
4
votes
0
answers
168
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Can nonflat deformations of singularities always produce Cohen-Macaulay rings?
To make the question in the title precise, let me phrase it like this. Consider a complete local ring
$$ A := \mathbb{C}[[x_1, \dotsc, x_n]]/(f_1, \dotsc, f_m) $$
and, for definiteness, assume that $...
- 2,663
3
votes
0
answers
992
views
Definition of Q gorenstein variety
I have a question about the definition of Q-Gorenstein variety.
I saw a definition of Q-Gorenstein variety：for a normal variety $X$, it's Q-Gorenstein if the canonical divisor is Q Cartier. I wonder ...
- 623
2
votes
0
answers
108
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Deformation to normal cone of the exception divisor of a log-resolution
I am reading the paper Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink due to G. Guibert, F. Loeser, and M. Merle. The main tool, like a lot of papers in ...
- 893
2
votes
0
answers
61
views
Test rational singularities after forming invariants
Let $R$ be a normal local domain of dimension $2$ and odd residue characteristic endowed with the action of the finite group $G \cong \mathbb{Z}/2\mathbb{Z}$. Suppose that the ring of invariants $R^G$ ...
- 407
1
vote
0
answers
242
views
Smooth normalization and blow-up of the exceptional locus
Let $n:\widetilde X\rightarrow X$ be the normalization of a complex (quasi-projective) variety $X$. Assume $\widetilde X$ is smooth, that $n$ is an isomorphism outside a smooth connected subvariety $Y\...
- 1,463
1
vote
0
answers
179
views
Spivakovski-Popescu-Neron desingularisation
For $A \colon= {\Bbb F}_p[[X_1,...,X_d]]$, by generalising Popescu-Neron's method, Spivakovski proved that $A$ is written by smooth sub-algebras. That is,
$A \cong \underset{\lambda \in \Lambda}{\...
- 781
0
votes
0
answers
195
views
Nice small resolution and normality of blow-up
Let $X$ be a complex variety whose singular locus is a smooth variety $Z$.
Let $f:Y\rightarrow X$ be a small resolution of $X$ such that $f^{-1}(z)$ is smooth for any $z\in Z$ and $\dim(f^{-1}(z))$ is ...
- 1,463