Timeline for lines on quintic del Pezzo 3-fold of degree 5
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2020 at 16:32 | comment | added | L. Xie | @Enrico Thanks, if I take $x_{12}=x_{34}$, $x_{13}=x_{45}$, $x_{23}=x_{15}$, then by a calculation I get two nonintersecting lines: one joining $( x_{14}=1,x_{ij}=0)$ and $( x_{12}=1,x_{ij}=0)$, the other joining $( x_{24}=1,x_{ij}=0)$ and $( x_{25}=1,x_{ij}=0)$. This should solve the question. | |
| Mar 14, 2020 at 14:31 | comment | added | Enrico | @L.X by the way, this might help mathoverflow.net/questions/323095/… | |
| Mar 14, 2020 at 14:06 | comment | added | Enrico | With these choices (if you pick the coefficients general enough) the correspondent variety will be a smooth, generic example of $V_5$ | |
| Mar 14, 2020 at 13:48 | comment | added | L. Xie | @Enrico You mean picking the hyperplanes in this way define the same variety V5? | |
| Mar 14, 2020 at 13:43 | comment | added | Enrico | @L.X in this case you should be safe by picking three of $x_{i,j}+x_{k,l}$ (with $i \neq j \neq k \neq l$, all five indexes involved and appropriate different coefficients). | |
| Mar 14, 2020 at 13:21 | comment | added | L. Xie | @Enrico $V(5)$ can be obtained as the intersection of $Gr(2,5)$ with $3$ hyperplanes in general position. Which hyperplanes should they be? | |
| Mar 12, 2020 at 21:36 | answer | added | L. Xie | timeline score: 4 | |
| Mar 9, 2020 at 16:35 | review | Close votes | |||
| Mar 14, 2020 at 3:04 | |||||
| Mar 9, 2020 at 14:12 | vote | accept | CommunityBot | ||
| Mar 8, 2020 at 22:13 | comment | added | Enrico | Just an extra comment: the five quadrics you are mentioning are way non general by obvious reasons. They are given by the 4-Pfaffians of the 5x5 skew matrix with the linear form $x_{i,j}$ at the $(i,j)$ entry. This is not directly connected to the question (which Sasha already solved), but might be relevant if you keep working with this particular variety. | |
| Mar 8, 2020 at 20:56 | answer | added | Sasha | timeline score: 4 | |
| Mar 8, 2020 at 20:41 | history | asked | anon | CC BY-SA 4.0 |