Timeline for Chern classes of a blow-up at a point
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 30, 2012 at 11:54 | comment | added | Johannes Nordström | $p^*(c_2(X))\cdot E$ is the integral of $p^*(c_2(X))$ over $E$. But $p$ restricted to $E$ is the constant map. | |
| Mar 30, 2012 at 11:41 | comment | added | gio | I am interested in when $X$ is a 3-fold and when the hyperplane section $H_{\widetilde{X}}$ of $\widetilde{X}$ is $p^{\ast}(H_{X})-E$ ($E$ the exceptional divisor). By Georges Elencwajg's answer I see $c_2(\widetilde{X})=p^{\ast}(c_2(X))$ and hence $\deg(c_2(\widetilde{X}))=c_2(\widetilde{X})\cdot (p^{\ast}(H_{X})-E)=c_2(X)\cdot H_{X}-p^{\ast}(c_2(X))\cdot E$, but but why you say that $p^{\ast}(c_2(X))\cdot E=0$? | |
| Mar 30, 2012 at 11:03 | history | answered | Johannes Nordström | CC BY-SA 3.0 |