Timeline for Techniques for showing that a curve is not smoothable

4 events

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Dec 3, 2012 at 18:59	comment	added	Charles Staats		Additional note: I've just looked up the definition of "Hirzebruch surface," and actually my "more basic example" is a special case of your example.
Dec 3, 2012 at 17:04	comment	added	Charles Staats		Edit: Probably, I mean to say that the general curve cannot be infinitesimally deformed to be irreducible. (But some points of the moduli component might lie in the closure of the space of irreducible curves.)
Dec 3, 2012 at 16:58	comment	added	Charles Staats		I'm familiar with this technique in the case of surfaces--a more basic example is to take $X$ to be the blowup of $\mathbb P^2$ at a point, and consider reducible curves that have negative intersection number with the exceptional divisor $E$. But I have two questions: 1. Can this sort of argument be applied if the ambient $X$ is not a surface? 2. Is there any hope for this sort of argument if we want to show that the general curve is reducible on an irreducible component of the moduli space (but not the whole connected component)?
Dec 3, 2012 at 12:12	history	answered	Jason Starr	CC BY-SA 3.0