Timeline for support of embedded points in a curve
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 10, 2014 at 23:23 | comment | added | NotNow | I am thinking in constructing curves $C$ with a given Hilbert polynomial by adding embedded points to another curve $\tilde{C}$. For example: Given a smooth plane cubic $\tilde{C}$ can I add an appropriate embedded point $l_P$ for obtaining a curve $C$ parametrized by the Hilbert scheme associated to $3t+1-d$ for any $d >0$? Can I add the point $l_p$ anywhere on $\tilde{C}$? | |
| Aug 10, 2014 at 22:05 | comment | added | Will Sawin | $l_p$ is necessarily a singular point of $C$.... | |
| Aug 10, 2014 at 20:12 | comment | added | Karl Schwede | Can you say some more information about how $C$ is given to you? Is it presented to you via a certain number of relations? Is it the image of something? Of course as Cantlog was saying, the embedded points are singular points of $C$ but I'm not sure how to say much more than that with the information given. | |
| Aug 10, 2014 at 19:07 | comment | added | NotNow | Thank you for the example. If you know of a weaker statement or a restriction on the support of $l_p$... I will appreciated it. | |
| Aug 10, 2014 at 19:05 | history | edited | NotNow | CC BY-SA 3.0 |
added 180 characters in body; edited title
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| Aug 10, 2014 at 19:03 | comment | added | abx | Your statement is not true, take $C\subset \mathbb{P}^2$ defined by $x^2=xy=0$. This gives the line $x=0$ with an embedded point at the origin. | |
| Aug 10, 2014 at 18:33 | history | asked | NotNow | CC BY-SA 3.0 |