Timeline for Degree of a projective scheme and its defining equations
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2013 at 15:08 | answer | added | answer_bot | timeline score: 1 | |
| S Nov 5, 2013 at 16:06 | history | suggested | IMeasy | CC BY-SA 3.0 |
changed format of the question
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| Nov 5, 2013 at 15:57 | answer | added | abx | timeline score: 4 | |
| Nov 5, 2013 at 15:56 | review | Suggested edits | |||
| S Nov 5, 2013 at 16:06 | |||||
| Nov 5, 2013 at 15:47 | comment | added | Jana | @Starr: Thank you for your comment. I am asking if there exist at least one non-zero polynomial of degree less than or equal to the degree of the scheme. I looked into the reference. Ex. 1.8.38 gives an answer to my question if $X$ is smooth. I am interested in the case when $X$ is not smooth (especially when $X$ is non-reduced). I do not totally understand how 1.8.37 helps me compare with the degree of the scheme. It would be very helpful if you could elaborate a bit more. | |
| Nov 5, 2013 at 15:26 | comment | added | Jana | @IMeasy: I meant for ANY projective scheme with the above mentioned properties. | |
| Nov 5, 2013 at 15:18 | comment | added | Jason Starr | Do you really want to ask only if there exists a polynomial in $I_X$ of degree $\leq d$? Of course I assume that you are asking about a non-zero polynomial. However, you could ask for much more, e.g., a collection of polynomials that set-theoretically / scheme-theoretically define $X$. I recommend that you take a look at Def. 1.8.37, p. 111, of Lazarsfeld's "Positivity in Algebraic Geometry, I", as well as the follow-up discussion. | |
| Nov 5, 2013 at 15:06 | comment | added | IMeasy | Yes, think about the twisted cubic in $P^3$. Its ideal is generated by 3 quadrics. | |
| Nov 5, 2013 at 14:53 | history | asked | Jana | CC BY-SA 3.0 |