Timeline for Equality of chern classes and isomorphism
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2010 at 17:03 | vote | accept | TonyS | ||
| Oct 30, 2010 at 15:06 | comment | added | Arend Bayer | Yes, effective means it is a non-zero sum of classes of subvarieties. You can deduce this from Grothendieck-Riemann-Roch - the key point is that the Todd class always starts with 1 in the top degree. However, a better argument is to use Hirzebruch-Riemann-Roch: if the Chern character is trivial, then the Hilbert polynomial is trivial by HRR, hence the sheaf is trivial. | |
| Oct 29, 2010 at 15:21 | comment | added | TonyS | Thanks, that's interesting and more general. What does effective mean in this case, e.g. in the Chow ring? $ch_d(Q)$ is a sum of codimension d subvarieties, and all coefficient are non negative? And how can i see that $ch_d(Q)$ has to be effective in this case? – | |
| Oct 29, 2010 at 15:18 | history | edited | Arend Bayer | CC BY-SA 2.5 |
added 51 characters in body
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| Oct 29, 2010 at 15:07 | history | answered | Arend Bayer | CC BY-SA 2.5 |