Timeline for Is the set of surfaces over Spec Z with ample canonical sheaf empty

Current License: CC BY-SA 3.0

10 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Jan 25, 2013 at 18:16	history	edited	Ariyan Javanpeykar	CC BY-SA 3.0	edited title
Jan 18, 2013 at 20:10	history	edited	Ariyan Javanpeykar	CC BY-SA 3.0	added 106 characters in body
Jan 18, 2013 at 20:07	vote	accept	Ariyan Javanpeykar
Jan 14, 2013 at 21:24	answer	added	Sándor Kovács		timeline score: 9
Jan 14, 2013 at 13:49	comment	added	Jason Starr		There is a phenomenon in fiber dimension $2$ that does not occur for fiber dimension $1$. Have you heard of "small resolutions" of threefold double point singularities? For instance, the hypersurface of $\mathbb{P}^3_{\mathbb{Z}_p}$ (with $p$ an odd prime) with defining equation $X_1^2 - p^2X_0^2 -X_2X_3$ is clearly singular at the in the closed fiber with homogeneous coordinates $[X_0,X_1,X_2,X_3] = [1,0,0,0]$. However, there is a birational modification (only in the closed fiber) that is smooth over $\text{Spec} \mathbb{Z}_p$.
Jan 14, 2013 at 10:21	comment	added	Damian Rössler		Dear Ariyan, could you give references for Th. 1-2-3 ?
Jan 13, 2013 at 22:55	comment	added	Ariyan Javanpeykar		@Will. Ha! You're right. I don't know why I didn't think of that while typing the question. Anyway, I'll leave it in the question for now. In fact, I'm also interested in "other" examples.
Jan 13, 2013 at 22:25	comment	added	Will Sawin		For question 2, if $C_1$ and $C_2$ are smooth curves over $\mathcal O_K$ with ample canonical bundle, then isn't $C_1\times C_2$ a smooth surface over $\mathcal O_K$ with ample canonical bundle? So you should be able to deduce the surfaces case from the curves case.
Jan 13, 2013 at 22:14	history	asked	Ariyan Javanpeykar	CC BY-SA 3.0