Timeline for First Chern class of canonical bundle ?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2013 at 17:59 | vote | accept | Youloush | ||
| May 24, 2013 at 21:28 | comment | added | Pavel Safronov | $H^2(X, \mathbf{Z})$ is the group of isomorphism classes of complex line bundles; the first Chern class of a vector bundle is the isomorphism class of the determinant bundle. This gives $c_1(T_X) = c_1(det T_X)$. Since $\omega_X = (det T_X)^{-1}$, you also get $c_1(\omega_X) = -c_1(det T_X)$. This works in pretty much any theory of Chern classes ($H^\bullet(X, \mathbf{Z})$, Chow groups, etc). | |
| May 24, 2013 at 16:50 | answer | added | Will Sawin | timeline score: 3 | |
| May 24, 2013 at 16:44 | history | asked | Youloush | CC BY-SA 3.0 |