Timeline for Is every smooth projective variety contained in a chain of smooth projective varieties of increasing dimension?
Current License: CC BY-SA 4.0
6 events
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| Aug 10, 2022 at 14:55 | comment | added | Jason Starr | This has come up before on MO (I can find a link). One obstruction to existence of a smooth hypersurface of degree $m$ containing $X$ is the image of the top Chern class of the normal bundle of $X$ inside the quotient of the Chow ring of $X$ by the principal ideal generated by $mc_1(\mathcal{O}(1))$. | |
| Aug 10, 2022 at 12:02 | comment | added | Gro-Tsen | Nevertheless, this is an interesting error (and instructive to me as I failed to detect it and probably would have if I had been refereeing a paper). | |
| Aug 10, 2022 at 9:14 | comment | added | Sasha | @abx: You are absolutely right, my argument is incorrect (see the edit). | |
| Aug 10, 2022 at 9:13 | history | edited | Sasha | CC BY-SA 4.0 |
added 342 characters in body
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| Aug 10, 2022 at 8:37 | comment | added | abx | I don't think that any smooth surface in $\mathbb{P}^4$ is contained in a smooth hypersurface, otherwise by Lefschetz theorem it would be a complete intersection? | |
| Aug 10, 2022 at 8:23 | history | answered | Sasha | CC BY-SA 4.0 |