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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
1
vote
A necessary and sufficient condition for a curve to have an $A_k$ singularity.
Although the above answer involving the local algebra and the Milnor number is correct, it is often very hard to apply in real situations. Especially if you have a general function with arbitrary coef …
3
votes
Corank 4 hypersurface singularities
I'm not sure that the definition at the beginning is correct. Let's assume that we have a holomorphic function germ $f : (\mathbb{C}^n,0) \to (\mathbb{C},0)$. Let $\mathscr{O}_n$ denote the local ring …
5
votes
Link of singularities
I think you will be interested in reading about the so-called Milnor map, and the so-called Minor Fibration Theorem.
The standard reference is John Milnor's book "Singular points of complex hypersurf …