This article asks the question: "Is every variety with quotient singularities a global quotient of a smooth variety by a finite group?"
Question. What branch of math does the concept of a global quotient belong to, and what does this phrase mean?
2026-03-29 12:03:39.1774785819
What does "global quotient" mean?
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The word "global" here is pleonastic: "global quotient" just means "quotient". In other words, the question is whether there exists a smooth variety $U$ and a finite group $G$ acting on $U$ such that your variety is the quotient of this action. The point of the word "global" is that the hypothesis of "quotient singularities" is exactly that this condition holds locally: every point in your variety has a neighborhood which is such a quotient (I think "neighborhood" means in the etale topology in this context but I might be wrong). So the question is whether you can go from knowing that your variety locally looks like such a quotient to knowing that it really is such a quotient ("globally").