## New answers tagged singularity-theory

5
votes

Accepted

### Singularities of contractions of extremal faces

In characteristic 0, the answer is well known. By assumption there is an ample divisor $A$ such that $K_X+\Delta+A$ cuts out $F$ and hence by the BPF theorem $K_X+\Delta+A\sim _{\mathbb Q,f}0$ and in ...

3
votes

Accepted

### Bishop's compactness theorem and convergence of analytic subset

Convergence is taken in Hausdorff sense,
though you can define the structure of a complex variety (the Barlet space)
on the set of cycles, taking every irreducible component with positive integer ...

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