Timeline for Do subsets of generators of a toric ideal generate a toric ideal?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Nov 12, 2010 at 20:53 | vote | accept | Timothy Wagner | ||
| Nov 12, 2010 at 20:53 | comment | added | Timothy Wagner | Thanks Vivek and Daniel for clearing that up. @Daniel, I have proved a result on the integral closure of certain products of ideals. I have also shown that it holds for certain kinds of toric ideals and it will hold for toric ideals satisfying the above property. I just wished to know if something like this was already known for toric ideals. I actually only need that the subsets of generators generate an integrally closed ideal. But integral closure is less tractable, so I decided to first see if the above holds. I am sorry I cannot go into more detail since I am yet to write up the article. | |
| Nov 12, 2010 at 18:43 | comment | added | Daniel Erman | @Timothy: Vivek's comment says it perfectly. I'm curious what led you to this question, by the way. | |
| Nov 12, 2010 at 7:41 | comment | added | Vivek Shende | Rephrasing the above argument: any two of any minimal set of generators will cut out a scheme of dimension 1. It must strictly contain the twisted cubic, since the ideal of the twisted cubic requires three generators. | |
| Nov 12, 2010 at 6:11 | comment | added | Timothy Wagner | Thanks for that example Daniel. I have seen examples like these where a particularly chosen generating set does not have the sought property (subsets of the generating set generating toric ideals). However, I am not sure if it's easy to show, even in the particular case of this example, whether no such minimal generating set exists. | |
| Nov 12, 2010 at 6:05 | history | answered | Daniel Erman | CC BY-SA 2.5 |