Timeline for Comparing the homogeneous defining ideals of multiple embeddings of a projective scheme
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2013 at 0:33 | comment | added | Allen Knutson | Consider a line and a conic in the plane, each an embedding of $P^1$. What sort of statement holds in this case that you would want to generalize? | |
| Jan 13, 2013 at 19:12 | comment | added | Martin Brandenburg | You ask when $\mathrm{Proj}(R/I)$ and $\mathrm{Proj}(R/I)$ are isomorphic over $k$. Probably there won't be any criterion which can be carried out in practice. But of course there are some necessary conditions (for example $\sqrt{I}$ prime iff $\sqrt{J}$ prime). | |
| Jan 13, 2013 at 19:05 | comment | added | Sasha | Assume that $X$ is a union of $N$ points. There is a huge number of embeddings of $X$ into $P^n$ (the open part of the Hilbert scheme $Hilb^N(P^n)$). The ideals defining them are pretty different. | |
| Jan 13, 2013 at 18:14 | history | asked | Nick Switala | CC BY-SA 3.0 |