Timeline for How would you call a subscheme of a smooth $S$-scheme?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 23, 2013 at 14:53 | comment | added | Jacob Bell | I think quasismooth has a meaning in derived geometry as well, like perfect cotangent complex concentrated in degrees -1 and 0. Also, Kai Behrend in his Annals paper "DT-type invariants via microlocal geometry" calls your varieties embeddable as well. | |
| Feb 23, 2013 at 8:35 | history | edited | Mikhail Bondarko | CC BY-SA 3.0 |
Upd. added.
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| Feb 23, 2013 at 8:23 | comment | added | anon | Not good --- google came up with 25,300,000 references, the first of which defined a projective variety to be quasismooth if its affine cone is smooth away from 0. "Smoothly embeddable", abbreviated to "emmeddable" if you wish, sounds better. | |
| Feb 23, 2013 at 7:56 | comment | added | Andrew Stout | I've seen the following definition of quasi-smooth floating around: locally free kähler differentials $\Omega_{X/S}$ and $X/S$ flat (where X/S has no finiteness condition -- e.g., $X/S$ may not be of finite type). Perhaps a better name for this is pro-smooth as I could imagine the central question here is when is $X$ pro-representable by smooth schemes of finite type over $S$. Nevertheless, embeddable is better. | |
| Feb 23, 2013 at 7:33 | comment | added | Sasha | I think Hartshorne in "Residues and Duality" calls it "embeddable". | |
| Feb 23, 2013 at 6:32 | history | asked | Mikhail Bondarko | CC BY-SA 3.0 |