Timeline for When is an algebraic space a scheme?
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| Nov 8, 2009 at 15:59 | comment | added | David Zureick-Brown | One is David Smyth's thesis. Its similar though, he gives alternative compactificaitons of $\bar{M_{g,n}}$ and shows that they have projetive coarse moduli spaces (here GIT doesn't work). | |
| Nov 8, 2009 at 15:36 | comment | added | mdeland | Ah, cool! Doing a little research I see that Koll\'ar has done exactly this in his paper "Projectivity of Complete Moduli". You let $D$ to be a power of the relative dualizing sheaf. Then for curves $C$ not contained in the boundary it's more or less clear the Nakai-Moishezon condition is satisfied and for curves contained in the boundary you work a little harder but it's still true. He also applies this to compactifications of surfaces of general type. Are there other known applications of this method? | |
| Nov 8, 2009 at 3:51 | history | answered | David Zureick-Brown | CC BY-SA 2.5 |