Timeline for Complete intersections in toric varieties
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2018 at 16:33 | comment | added | user120812 | @PiotrAchinger Is it expected, ie. conjectured, that every smooth projective variety is a set theoretic complete intersection in a toric variety? At least I know of no example of a smooth projective variety that isn't. | |
| Mar 19, 2018 at 9:53 | comment | added | Simon L Rydin Myerson | Ah sorry, I somehow read "let $X$ be a smooth projective complete intersection", which made the question trivial. | |
| Mar 19, 2018 at 9:43 | comment | added | Piotr Achinger | The question becomes more interesting if you add "set-theoretic". Then I think very little is known even for curves. | |
| Mar 19, 2018 at 9:29 | vote | accept | CommunityBot | ||
| Mar 19, 2018 at 9:29 | vote | accept | CommunityBot | ||
| Mar 19, 2018 at 9:29 | |||||
| Mar 19, 2018 at 9:04 | comment | added | Francesco Polizzi | I do not understand. Not all smooth projective varieties are global complete intersections in a projective space, for instance because in higher dimension a complete intersection in $\mathbb P^n$ is necessarily simply connected. | |
| Mar 19, 2018 at 9:02 | answer | added | Francesco Polizzi | timeline score: 12 | |
| Mar 19, 2018 at 8:47 | comment | added | Simon L Rydin Myerson | Projective $n$-space is a smooth projective toric variety, and to me "global complete intersection" is just another way to say "complete intersection" (as opposed to "local complete intersection"). So the answer is yes, unless you mean something different by "global complete intersection". | |
| Mar 19, 2018 at 8:17 | history | asked | user120812 | CC BY-SA 3.0 |