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edited Oct 21, 2009 at 4:24

David Zureick-Brown

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Can a singular Deligne-Mumford stack have a smooth coarse space?

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asked Oct 21, 2009 at 3:05

David Zureick-Brown

10.5k
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39
96

Can singular Deligne-Mumford stack have a smooth coarse space?

Let XX be a Deligne-Mumford stack and let XX \to X be a coarse moduli space. Suppose that X is smooth. Is XX smooth? If not, what is an example? What if XX is of finite type over C (the complex numbers)? What are conditions we can put on XX to make this true?

ag.algebraic-geometry stacks