Timeline for Is the moduli space of genus three smooth quartics affine?

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Dec 23, 2012 at 16:29	comment	added	Masse		@Jason. That's what I was looking for indeed. Any nonempty effective divisor on $\mathbf P^{14}$ is ample.
Dec 23, 2012 at 16:27	comment	added	Masse		@Olivier. You're right. I didn't mean to say that. Rather, more generally, the moduli space of smooth hypersurfaces of degree $d$ in $N$-projective space is affine if $d>N+1$.
Dec 23, 2012 at 14:24	comment	added	Olivier Benoist		Beware that analogous results for smooth complete intersections do not hold in general. For instance, the moduli space of non-hyperelliptic genus $4$ curves, that is the moduli space of smooth complete intersections of degrees $(2,3)$ in $\mathbb{P}^4$ is not affine, beacuse it contains complete curves.
Dec 23, 2012 at 13:53	comment	added	Jason Starr		Every nonempty divisor in $\mathbb{P}^{14}$ is ample and its complement is affine. Is that what you are looking for?
Dec 23, 2012 at 13:36	history	asked	Masse	CC BY-SA 3.0