Timeline for Hypersurface of complex projective space
Current License: CC BY-SA 3.0
14 events
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| Mar 27, 2017 at 6:28 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| Dec 4, 2016 at 23:26 | history | edited | Francesco Polizzi | CC BY-SA 3.0 |
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| May 22, 2011 at 15:13 | vote | accept | Yunhyung Cho | ||
| Oct 15, 2010 at 7:39 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
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| Oct 14, 2010 at 8:49 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
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| Oct 14, 2010 at 6:36 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
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| Oct 14, 2010 at 6:09 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
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| Oct 14, 2010 at 6:01 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
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| Oct 13, 2010 at 21:36 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
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| Oct 13, 2010 at 21:31 | comment | added | Francesco Polizzi | Yes, that's true. However, I find this proof interesting since its provides the Betti numbers for hypersurfaces of any degree d, not only for quadrics, showing that in higher degrees, when n is odd, one always has a non-zero odd Betti number. I have edited the answer to make this more clear. | |
| Oct 13, 2010 at 21:29 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
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| Oct 13, 2010 at 19:22 | comment | added | Tom Goodwillie | I don't know whether the question was meant to include non-smooth quadric hypersurfaces, but the answer is the same for them: their (co)homology is free and concentrated in even degrees. In fact, every singular quadric $X$ in $\mathbb P^{n+1}$ is the projective cone on some quadric $Y$ in $\mathbb P^{n}$, making $H_k(X)$ isomorphic to $H_{k-2}(Y)$ for every $k>0$. | |
| Oct 13, 2010 at 19:05 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
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| Oct 13, 2010 at 18:49 | history | answered | Francesco Polizzi | CC BY-SA 2.5 |