Timeline for Degeneration of curves in smooth families
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 24, 2023 at 21:26 | vote | accept | user45397 | ||
| Jun 24, 2023 at 11:33 | answer | added | Jason Starr | timeline score: 2 | |
| Jun 23, 2023 at 20:35 | comment | added | Jason Starr | Here is a counterexample. Let $\mathcal{X}$ be a family of Hirzebruch surfaces whose generic fiber is isomorphic to $\mathbb{P}^1\times \mathbb{P}^1$ specializing to a Hirzebruch surface that is a minimal (crepant) resolution of a singuar quadric cone in $\mathbb{P}^3$. Consider the curve class whose specialization is the sum of a "fiber" curve class and the "directrix" curve class. Then $B$ is just $\mathbb{P}^1_R$. The curves on the generic fiber are integral (smooth, rational curves), but on the special fiber they are all reducible. | |
| Jun 20, 2023 at 23:44 | history | asked | user45397 | CC BY-SA 4.0 |