Timeline for inverse image in the blowup
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2013 at 15:08 | comment | added | Karl Schwede | Unfortunately, that is not the case. The product and intersection of ideals can be quite different even in that case. For instance, consider $k[x,y,z]$ and $I_1 = (x,y), I_2 = (y,z)$. Then $$ I_1 \cdot I_2 = (xy, xz, yz, y^2) $$ but $$ I_1 \cap I_2 = (xy, xz, yz, y). $$ The blowups are different too. | |
| Jun 12, 2013 at 14:18 | comment | added | marker | Thank you very much. If I understand correctly, everything should work in a nice way if $Z_1$ and $Z_2$ are both integral. Am I right? | |
| Jun 12, 2013 at 12:41 | history | answered | Karl Schwede | CC BY-SA 3.0 |