Timeline for Putting two complete varieties in a family over the projective line
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| May 10, 2012 at 1:01 | comment | added | Sándor Kovács | Yes, this sounds right. On the other hand, I don't know how you can decide that they belong to the same irreducible component of the Hilbert scheme other than producing such a family, so this condition may not be helpful at all. | |
| May 9, 2012 at 17:07 | vote | accept | hadimath | ||
| May 9, 2012 at 17:06 | comment | added | hadimath | If we relax the condition that $X$ and $Y$ should live in a family over $\mathbb{P}^1_k$, and only require that there should live in a family over some curve (possibly satisfying some additional conditions e.g. smooth), would the answer then be positive? In other words, instead of "rational connectivity", we require "algebraic connectivity". I believe in this case, any two points on the same irreducible component of the Hilbert scheme can be connected by a curve. | |
| May 8, 2012 at 8:00 | history | answered | Sándor Kovács | CC BY-SA 3.0 |