Timeline for Quotienting a scheme by finite group
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2013 at 12:11 | comment | added | Francesco Polizzi | The quotient of a smooth curve for a finite group of automorphism is smooth. The point is that quotient singularities are normal, so they can only occur in codimension $\geq 2$. | |
| Sep 24, 2013 at 12:10 | comment | added | S. Carnahan♦ | If you take the quotient of a smooth curve by a finite group, you will get a smooth curve. | |
| Sep 24, 2013 at 11:40 | history | edited | Anon | CC BY-SA 3.0 |
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| Sep 24, 2013 at 11:36 | comment | added | Anon | @francesco-polizzi : Actually I was only looking at curves. Is it the case that quotient singularities won't occur on schemes (or analytic spaces) corresponding to curves? | |
| Sep 24, 2013 at 10:02 | comment | added | Francesco Polizzi | I do not complete understand what you means by sayng "are the singularities visibles?". Are you asking whether the quotient space (scheme or analytic variety) can be singular? Of course it can be. The quotient of $\mathbb{C}^2$ by the involution $(x, y) \cong (-x, -y)$ is isomorphic to a quadric cone (look at the ring of invariants). The key words are "Quotient singularities". There is a huge literature about. | |
| Sep 24, 2013 at 8:29 | history | asked | Anon | CC BY-SA 3.0 |