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Results tagged with singularity-theory
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user 50468
Singularities in algebraic/complex/differential geometry and analysis of ODEs/PDEs. Singular spaces, vector fields, etc.
0
votes
Applying analytic coordinate changes to singular function germs
Analytic change of coordinates in $(\mathbb{C}^3,0)$ must take $0$ to $0$. So they are induced by (local)
$\mathbb{C}$-automorphisms of $\mathcal{O}_{\mathbb{C}^3,0}=\mathbb{C}\{x,y,z\}$ taking $\math …
- 375
1
vote
Scheme-theoretic image and delta-invariants
Without any stronger hypothesis connecting $f$ and $g$ you should not expect that to happen.
The simplest instance is when $(X,o)$ is alrealdy non singular, say dimension 2: $(\mathbb{C}^2,o)$. In thi …
- 375
8
votes
Accepted
General conditions for normality of blow-up
Let $X=Spec(R)$. Blowing-up $Z=V(I)$ is the same as to look at $Proj$ of the graded ring $R[It]=\oplus_{j\geqslant 0} I^jt^j\subset R[t]$, the Rees ring associated to $I$.
Assume $R$ is a domain, inte …
- 375