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Singularities in algebraic/complex/differential geometry and analysis of ODEs/PDEs. Singular spaces, vector fields, etc.
5
votes
Accepted
Is resolution of singularities effective?
Yes, in the sense that resolution of singularities is implemented in the computer algebra package Singular. See the manual of Singular for references. (There might be other/better references.) However …
4
votes
Smooth in codimension-k and the weight filtration
Assume for simplicity that X is projective. Then you have a Gysin sequence
$H^i_c(X_{smooth})\to H^i_c(X)\to H^i_c(X_{sing})\to\dots$
If $X_{sing}$ has small dimension then for large $i$ you find iso …
11
votes
Accepted
Are orbifold singularities canonical?
For quotient singularities there is the so-called Reid-Tai criterion to check whether the singularity is canonical or not.
Suppose $G$ is a finite subgroup of $GL_n(\mathbb{C})$ without quasi-reflecti …
1
vote
Accepted
A condition on isolated singularity
Assume that $F$ is quasihomogeneous.
A condition on $F$ would be the following.
For each $k$ write $F=x_kG+H_k(x_1,\dots,x_{k-1},x_{k+1},\dots, x_N)$. Then $H_k$ is quasihomogeneous.
If for each $k$ …