Timeline for Clean Proofs of Properties of Projective Space
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 19, 2011 at 4:58 | comment | added | Lennart Galinat | @Anton: For a reduced algebraic variety over a field one can show by hand that its global sections are a finite dimensional vector space, Liu does it this way in his book. Then the fact that P^n is geometrically integral shows that its global sections are a one-dimensional. | |
| Oct 19, 2011 at 1:28 | comment | added | Daniel Litt | Now that I think about it, you're right, that's essentially the argument I know. Furthermore, I think I'd actually need that $\mathbb{P}^n$ was reduced (which I think can be done from the universal property but I haven't worked out). In any case, one can at least check properness and connectedness :). | |
| Oct 19, 2011 at 1:13 | comment | added | Anton Geraschenko | I like it, but I'm skeptical. To prove that proper connected things have no global sections, don't you use Chow's lemma to reduce to the case of projective space? | |
| Oct 18, 2011 at 22:19 | history | answered | Daniel Litt | CC BY-SA 3.0 |