Timeline for Intuition for coordinate patches on Proj of a graded ring.
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 9, 2013 at 12:22 | vote | accept | Daniel Barter | ||
| Jun 5, 2013 at 1:26 | comment | added | François Brunault | See the answers to mathoverflow.net/questions/41624/… | |
| Jun 5, 2013 at 1:04 | history | edited | Daniel Barter | CC BY-SA 3.0 |
deleted 15 characters in body
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| Jun 5, 2013 at 0:57 | comment | added | Allen Knutson | A ring $R$ is $\mathbb Z$-graded iff it carries an action of the multiplicative group (proof: define $R_i$ to be the subspace where $z\cdot$ acts by $z^i$). Then, that group will also act on ${\rm Spec}\ R$. Then for the first question, you need to look past the obvious inclusion $R_0 \to R$ to the less obvious quotient $R \to R_0$. This only works because $R$ is $\mathbb N$-graded, not just $\mathbb Z$-graded. | |
| Jun 5, 2013 at 0:51 | history | edited | Daniel Barter | CC BY-SA 3.0 |
added some content
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| Jun 4, 2013 at 21:59 | answer | added | David Mahone | timeline score: 1 | |
| Jun 4, 2013 at 21:46 | answer | added | pinaki | timeline score: 4 | |
| Jun 4, 2013 at 21:37 | comment | added | Daniel Barter | Hmm this sounds interesting as it is much closer to the "classical" definition of projective space. Two thinks I am a little unsure about though: How is $ {\rm spec} R_0 $ closed subset of $ {\rm spec } R $? How do you mod out by scaling? | |
| Jun 4, 2013 at 21:28 | comment | added | Allen Knutson | This is more about $\rm Proj$ than about its structure sheaf, but I much prefer the definition ${\rm Proj}\ R = ({\rm Spec}\ R \setminus {\rm Spec} R_0)/$scaling to the gluing construction. (And in fact, I essentially never glue schemes together along open subschemes.) | |
| Jun 4, 2013 at 21:00 | history | asked | Daniel Barter | CC BY-SA 3.0 |