Timeline for Higher dimensional Bezout via Hilbert polynomials: a reference
Current License: CC BY-SA 3.0
13 events
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| Mar 5, 2013 at 22:16 | vote | accept | aglearner | ||
| Mar 4, 2013 at 11:37 | comment | added | aglearner | Dear Sandor, thank you for this very detailed answer! This helps me to understand better the nature of regular sequences. This also indicates me I guess that I will need to be less ambitious in what to say to students :)... | |
| Mar 4, 2013 at 11:12 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Mar 4, 2013 at 8:28 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Mar 4, 2013 at 8:06 | comment | added | Sándor Kovács | Hailong, you probably meant that there might be an associated component that has smaller dimension? That's sort of the same problem as the one you mentioned with regard to Claim 2. I'll edit accordingly. | |
| Mar 4, 2013 at 8:04 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Mar 4, 2013 at 7:59 | comment | added | Sándor Kovács | [Hartshorne, Ex.I.1.9, page 8]. The proof is as I said above by Krull's principal ideal theorem. | |
| Mar 4, 2013 at 7:57 | comment | added | Sándor Kovács | Hailong, that can never happen. In general, it is possible that $Z(f_1,\dots,f_r)$ has an irreducible component that has dimension larger than $n-r$, but it can never be smaller than that. | |
| Mar 4, 2013 at 7:55 | history | edited | Sándor Kovács | CC BY-SA 3.0 |
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| Mar 4, 2013 at 7:50 | comment | added | Hailong Dao | Dear Sándor, what I did not understand in Claim 1 was that while $Z(f_1,...,f_r)$ is of dimension $n-r$, it may have component of smaller dimensions. Perhaps I was missing something? | |
| Mar 4, 2013 at 7:47 | comment | added | Sándor Kovács | Dear Hailong, I am not sure I see your problem with Claim 1. Regarding Claim 2, you are right. I was trying to avoid using "unmixedness" but it was on my mind... I meant this in the situation of the question. I guess I'll have to revise this.... | |
| Mar 4, 2013 at 7:10 | comment | added | Hailong Dao | Dear Sándor, Claim 1: why does any component have same dimension? And Claim 2: for $x$ to be a NZD you need it to be outside all associated primes, not just minimal. | |
| Mar 4, 2013 at 6:26 | history | answered | Sándor Kovács | CC BY-SA 3.0 |