Timeline for Automorphism group of a scheme
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2011 at 10:51 | comment | added | Sándor Kovács | Dan & THC: I included another answer below regarding when extending automorphisms to the ambient projective space works. | |
| Feb 15, 2011 at 15:38 | vote | accept | THC | ||
| Feb 15, 2011 at 15:27 | vote | accept | THC | ||
| Feb 15, 2011 at 15:38 | |||||
| Feb 15, 2011 at 15:26 | comment | added | THC | I guess that in general, one cannot show that any automorphism extends to one of the ambient projective space, but the class that I am interested in has this property :-) | |
| Feb 15, 2011 at 15:23 | comment | added | THC | Hi, Dan - yep, I knew (it's only "a for instance sentence") :-) | |
| Feb 15, 2011 at 12:04 | comment | added | Dan Petersen | Also, if you had asked Torsten or Sándor the same question, you would've gotten an authoritative answer. :p | |
| Feb 15, 2011 at 11:59 | comment | added | Dan Petersen | Not that I know of. Maybe you can show that any automorphism extends to the ambient projective space (by cooking up an equivariant ample line bundle?), and then embed the automorphism group scheme in $\operatorname{Aut} \mathbf{P}^n = \mathrm{PGL}(n+1)$. P.S. Perhaps you already know this and I am talking down to you, but when you work over a field, the adjective flat can be omitted -- every morphism to the spectrum of a field is flat. D.S. | |
| Feb 15, 2011 at 9:28 | comment | added | THC | Thanks ! Is there a "direct" way to do it for flat and projective schemes, that is, without using the Hilbert scheme ? (For instance when one works with base a field.) | |
| Feb 11, 2011 at 12:57 | history | edited | Dan Petersen | CC BY-SA 2.5 |
added 635 characters in body; added 9 characters in body
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| Feb 11, 2011 at 12:02 | comment | added | Daniel Loughran | Forgive the naive question, but is there a nice explanation of why being an automorphism is an open condition? | |
| Feb 10, 2011 at 16:21 | history | answered | Dan Petersen | CC BY-SA 2.5 |