Timeline for Is there an algebraic way to characterise the ordinary integral flags?
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| Feb 24, 2016 at 15:50 | comment | added | Robert Bryant | @GiovanniMoreno: I'll respond to both of your comments in this one comment: First, any condition one writes down that tests for a flag to be ordinary is going to be equivalent to Cartan's Test in some way or another. While many people have looked for ways to describe it in various terms using ideas from commutative algebra, in my opinion, none of these has been very useful in practice. Second, it can happen that the non-ordinary integral flags of $\mathcal{I}$, while closed in the variety of all flags, are not the integral flags of any ideal $\mathcal{J}$. | |
| Feb 24, 2016 at 15:03 | comment | added | Giovanni Moreno | Concerning your second remark, I agree with the fact that being an ordinary integral flag is an "open condition" (or, at least, "not closed"). However, I could rephrase my question, by asking how to construct the ideal of the complement, i.e., the (closed) variety of non-ordinary integral flags. (On a completely unrelated matter: Pawel really needs an answer from you). | |
| Feb 24, 2016 at 14:56 | comment | added | Giovanni Moreno | I asked this question after I finished reading Chap 3 of the book, being not satisfied by the Cartan's test, in this sense. Given a curve, I can decide whether a point belongs to its secant variety, by performing some test involving geometric manipulations; however, if you want to study the secant variety as a variety on its own, then an its algebraic description would be more desirable (even indispensable): to this end I can take, e.g., a parametrisation of the curve and obtain from it a parametrisation of the secant. I would like something like this for the variety of ordinary integral flag! | |
| Feb 24, 2016 at 12:03 | history | answered | Robert Bryant | CC BY-SA 3.0 |