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Let $(X,0)$ be a normal surface singularity. Suppose that it does not admit a smoothing.

Is it possible that there exists an isolated surface singularity $(Y,0)$ reduced near $0$ which is not irreducible and $(X,0)$ is one of its irreducible components and such that $(Y,0)$ does admit a smoothing? Is there some obstruction for this to happen?

Are these kind of questions treated somewhere?

Let $(X,0)$ be a normal surface singularity. Suppose that it does not admit a smoothing.

Is it possible that there exists an isolated surface singularity $(Y,0)$ which is not irreducible and $(X,0)$ is one of its irreducible components and such that $(Y,0)$ does admit a smoothing? Is there some obstruction for this to happen?

Are these kind of questions treated somewhere?

Let $(X,0)$ be a normal surface singularity. Suppose that it does not admit a smoothing.

Is it possible that there exists an isolated surface singularity $(Y,0)$ reduced near $0$ which is not irreducible and $(X,0)$ is one of its irreducible components and such that $(Y,0)$ does admit a smoothing? Is there some obstruction for this to happen?

Are these kind of questions treated somewhere?

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Smoothings of isolated non-irreducible surface singularities

Let $(X,0)$ be a normal surface singularity. Suppose that it does not admit a smoothing.

Is it possible that there exists an isolated surface singularity $(Y,0)$ which is not irreducible and $(X,0)$ is one of its irreducible components and such that $(Y,0)$ does admit a smoothing? Is there some obstruction for this to happen?

Are these kind of questions treated somewhere?