Timeline for When can one extend a flat family from a subscheme to the whole scheme?
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| Sep 30, 2010 at 23:21 | comment | added | Karl Schwede | Indeed, although people do sometimes do contractions of this sort in the analytic setting (I recall seeing this in Hodge theoretic contexts) if you are willing to work analytically and sufficiently locally. | |
| Sep 30, 2010 at 22:29 | comment | added | Owen Biesel | Right, that's in particular how it works for one point in $\mathbb{P}^1$. But just to elaborate on why it doesn't work for two lines in $\mathbb{P}^2$: there can't be a surjective map from $\mathbb{P}^2$ to the two lines, because $\mathbb{P}^2$ is irreducible and so must be its image. | |
| Sep 30, 2010 at 21:10 | history | answered | Karl Schwede | CC BY-SA 2.5 |