Timeline for Square of Generic Gorenstein ideal
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 13, 2023 at 18:21 | comment | added | Zach Teitler | There is an easy weaker statement: $(I_f^k)_{k(d+1)} = S_{k(d+1)}$ for some $k$. To see this, first of all, you have the hypothesis that $S/I_f$ is what Iarrobino calls "compressed", and it implies that $(I_f)_d = 0$. So the minimum degree generators of $I_f$ are in degree $d+1$. Gorenstein symmetry implies the maximum degree generators of $I_f$ are also in degree $d+1$. So $I_f$ is generated purely in degree $d+1$. Next: $I_f$ is $\mathfrak{m}$-primary for the irrelevant (homogeneous maximal) ideal $\mathfrak{m}$. So some $\mathfrak{m}^s \subset I_f$, and it implies my weaker claim. | |
| Nov 17, 2019 at 10:10 | comment | added | Hans | That would be very nice! | |
| Nov 16, 2019 at 6:21 | comment | added | Zach Teitler | I think it might be true in more than $3$ variables, too. (I only computed a few examples, so I'm not sure, but it seems to be correct.) | |
| Nov 14, 2019 at 20:47 | history | asked | Hans | CC BY-SA 4.0 |