Timeline for Quadric surfaces tangent to a cubic threefold along a line of first type
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 26, 2020 at 21:31 | vote | accept | AG learner | ||
| Nov 1, 2020 at 22:23 | history | edited | AG learner | CC BY-SA 4.0 |
edited title
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| Nov 1, 2020 at 21:53 | answer | added | AG learner | timeline score: 0 | |
| Nov 1, 2020 at 19:29 | comment | added | AG learner | Dear @Sasha, as the normal bundle $N_{L|X}$ is $\mathcal{O}_L\oplus \mathcal{O}_L$, the image of any nonzero section $s$ is a line in $\mathbb P^4$ which is disjoint from $L$ and union of family of disjoint lines $\cup_{0\le t\le 1}ts(L)$ is Zariski dense in a quadric surface, whose tangent spaces along $L$ are contained in $TX$. Two sections determine the same quadric surface if and only if one is a multiple to the other, so there is a $\mathbb PH^0(N_{L|X})\cong \mathbb P^1$-family of such quadric surfaces. Actually, I can find these equations now. I'll write a solution below. | |
| Nov 1, 2020 at 8:21 | comment | added | Sasha | How do you conclude that there is a $\mathbb{P}^1$-family of quadric surfaces in $\mathbb{P}^4$ tangent to $X$ along $L$? | |
| Nov 1, 2020 at 2:31 | history | edited | AG learner | CC BY-SA 4.0 |
added 1 character in body
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| Nov 1, 2020 at 2:26 | history | asked | AG learner | CC BY-SA 4.0 |