Timeline for Family of elliptic curves in $\mathbb P^3$
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 10, 2020 at 17:03 | answer | added | Libli | timeline score: 4 | |
| Apr 10, 2020 at 4:32 | comment | added | abx | Try to write down equations for an elliptic curve of degree 5 in $\Bbb{P}^3$, you'll understand why there is no easy answer. | |
| Apr 9, 2020 at 19:27 | comment | added | Alex M. | @user69559: It would help to know if $\mathcal C$ is $C$, and who is $B$. | |
| Apr 9, 2020 at 15:52 | comment | added | Will Sawin | I would still recommend you take this more general question, write it up carefully, and ask it on math stack exchange. | |
| Apr 9, 2020 at 10:02 | comment | added | Basics | Now I have edited the question so that the smoothed elliptic curve is not a complete intersection. | |
| Apr 9, 2020 at 9:55 | history | edited | Basics | CC BY-SA 4.0 |
deleted 56 characters in body
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| Apr 9, 2020 at 9:50 | comment | added | Basics | @abx, I got it! Maybe I simplified too much. The orginal problem I had in my mind is: for $p_1, p_2, \cdots, p_k$ in $\mathbb P^n$, I wanted to constuct an explicit smoothing of the union of lines: $$l_{12} \cup l_{23} \cup \cdots \cup l_{n1}$$ to an elliptic curve. | |
| Apr 9, 2020 at 9:34 | comment | added | abx | Not the union, the intersection! Just deform $Q'$ to a general quadric. Note that we are in $\Bbb{P}^3$, in case you didn't notice. | |
| Apr 9, 2020 at 9:30 | review | Close votes | |||
| Apr 12, 2020 at 5:01 | |||||
| Apr 9, 2020 at 9:26 | comment | added | Basics | @abx, I had tried in that way but what's next? $Q$ and $Q'$ need to intersect with each other at two points and one needs to deform the union of $Q$ and $Q'$ to a single elliptic curve. It is not clear to me how to proceed. | |
| Apr 9, 2020 at 9:14 | comment | added | abx | Write $C$ as an intersection of 2 quadrics, for instance, a smooth quadric $Q$ and the union $Q'$ of 2 tangent planes, and deform $Q'$. | |
| Apr 9, 2020 at 9:00 | comment | added | Sasha | This would be more appropriate on math.stackexchange | |
| Apr 9, 2020 at 8:45 | comment | added | Basics | No, it is not. It is related with my research( I simplified a little bit) Is it an easy question that can be on a homework? Then please give me an answer! | |
| Apr 9, 2020 at 8:42 | comment | added | Sasha | Is it your homework? | |
| Apr 9, 2020 at 8:40 | history | asked | Basics | CC BY-SA 4.0 |