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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 …
Remke Kloosterman's user avatar
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 …
Remke Kloosterman's user avatar
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 …
Remke Kloosterman's user avatar
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 $k$ …
Remke Kloosterman's user avatar