Timeline for What is the minimal degree of a smooth curves which is not on a cubic surface in $P^3$?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2013 at 21:22 | history | bounty ended | Nikita Kalinin | ||
| May 31, 2013 at 21:04 | history | bounty started | Nikita Kalinin | ||
| May 27, 2013 at 20:27 | comment | added | Charles Staats | Nikita: I have edited your question in an attempt to clarify your intent, as I now understand it. Obviously, you should feel free to modify/undo any or all of my edits. | |
| May 27, 2013 at 20:26 | history | edited | Charles Staats | CC BY-SA 3.0 |
clarified intent of question
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| May 27, 2013 at 18:30 | comment | added | Nikita Kalinin | to Charles Staats: Thank you! I just had in mind dimension computations: there is 20-dimensional space of rational curves degree 7 and 19-dimensional space of cubic surfaces. | |
| May 26, 2013 at 20:49 | answer | added | Charles Staats | timeline score: 11 | |
| May 26, 2013 at 20:12 | comment | added | Charles Staats | Not exactly. The claim is that if $C$ is a general rational curve of degree 7, then there is no cubic hypersurface containing $C$. There are some rather involved ways to see this by "pure thought," but one can also simply choose a degree 7 rational curve with random coefficients and compute (using Macaulay2, for instance) its homogeneous ideal. If you do this, you will see that the homogeneous ideal contains no polynomials of degree $\leq 3$. | |
| May 26, 2013 at 20:04 | history | edited | Nikita Kalinin | CC BY-SA 3.0 |
added 2 characters in body
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| May 26, 2013 at 20:03 | comment | added | Nikita Kalinin | and how to get it? It seems that the claim is that on a cubic there is no a one-dimensional family of rational curves of degree 7... | |
| May 26, 2013 at 19:22 | comment | added | Charles Staats | The minimum degree of a smooth rational curve that is not contained in any cubic surface is 7. | |
| May 26, 2013 at 19:15 | history | asked | Nikita Kalinin | CC BY-SA 3.0 |