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I would like to know applications of Resolution of Singularities. What are the benefit of resolving singularities of a variety by blow-up maps in a context outside of mathematics? I'm fine with both positive and zero characteristics cases. The only thing I know right now is a mathematical implication that every variety has a smooth birational equivalent, so for classifying varieties up to birational equivalence, we can focus on smooth varieties.

But I don't know any other applications. I wonder if is it useful in engineering or other places such as robotics etc. Any application would be interesting.

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