Timeline for Is every projective space curve a set-theoretic intersection of two surfaces? What is known about this question?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| yesterday | comment | added | Aurora | Could you please share what are the results in prime characteristic you are aware of? I googled, but couldn't find any? | |
| Jan 21, 2020 at 1:12 | answer | added | myzhang24 | timeline score: 8 | |
| Jan 21, 2020 at 0:58 | comment | added | myzhang24 | @Michael the twisted cubic is a set-theoretical complete intersection. The singular quadric and a cubic cuts out a multiplicity two structure on it. | |
| Dec 26, 2014 at 7:58 | comment | added | shamovic | @Mohan thanks, I've added irreducible to the statement of the question. I wonder just whether there are some general results. I've seen people constructing monomial curves that are set-theoretic intersection of two hypersurfaces, but I'd like something more general. | |
| Dec 26, 2014 at 7:56 | history | edited | shamovic | CC BY-SA 3.0 |
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| Dec 18, 2014 at 4:48 | comment | added | Mohan | Very little. I assume you meant connected, since a set-theoretic complete intersection curve is connected. @Michael, the twisted cubic is defined set-theoretically as the intersection of a quadric and a cubic. In $\mathbb{C}^3$, every smooth (actually local complete intersection) curve is a set-theoretic complete intersection, but in general, the problem is open. | |
| Dec 17, 2014 at 22:12 | comment | added | Michael | Maybe I misunderstood the question, wouldn't twisted cubic be a counterexample? | |
| Dec 17, 2014 at 18:08 | history | edited | shamovic | CC BY-SA 3.0 |
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| Dec 17, 2014 at 11:37 | history | asked | shamovic | CC BY-SA 3.0 |