Timeline for Limits of complex projective varieties in the Hausdorff topology on closed subsets of CP^n
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 16, 2015 at 14:44 | comment | added | Daryl Cooper | category_student: Thanks for telling me about Lojasiewicz inequality. I am a topologist and do not know any algebraic geometry. However it is not true that M and M' close implies V(M) is close to V(M') e.g. $M=\langle x^2y,xy^2\rangle$ and $M_k=\langle x^2y,xy^2+ (x+y)^3k^{-1} \rangle$. Then $M_k\to M$ as $k\to\infty$ but $V(M)$ and $V(M_k)$ have different dimensions. The problem seems to be there is a constant in the Lojasiewicz inequality that does not vary continuously with the data. | |
| Jul 16, 2015 at 3:11 | comment | added | Mariano Suárez-Álvarez | Ah. I am sorry. I thought you might be trying to be helpful. My mistake. | |
| Jul 16, 2015 at 3:08 | comment | added | category_student | No, they don't. I was too lazy to normalize things, but I am sure you can manage it in your head. | |
| Jul 16, 2015 at 2:45 | comment | added | Mariano Suárez-Álvarez | But homogeneous polynomials do not "take values" on points of projective space. | |
| Jul 16, 2015 at 2:21 | history | answered | category_student | CC BY-SA 3.0 |