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Kapranov gave a very nice desciption, over $\mathbb{C}$ of the moduli space of stable pointed rational curves $\overline{M}_{0,n}$ as a series of blow-ups of $P^{n-3}$. Does this, or a similar result, hold over other fields? e.g. positive characteristic, non algebraically closed, etc.

ps I am afraid one could only dream of this, over non alg closed fields...

flag	asked Oct 12 at 17:05 IMeasy 1,355●4●12

	what is the reference for Kapranov's result ? – Alexander Chervov Oct 13 at 12:50
	The paper is called "chow quotients of grassmannians 1". – Dan Petersen Oct 13 at 17:37
	@Alexander: there are also other realizations as a blow up, see Keel, Intersection theory of moduli spaces of stable n-pointed curves of genus 0. – IMeasy Oct 14 at 18:27

Dan Petersen · Accepted Answer · 2012-10-12 19:56:13Z UTC

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It seems to me Kapranov's methods are purely algebraic and that his description works verbatim over $\mathrm{Spec}(\mathbf Z)$.

answered Oct 12 at 19:56

Dan Petersen
10.1k●1●21●46

@Dan: thank you for answering, I have checked the paper and in fact it does seem that you are right. So probably he works over $\mathbb{C}$ just for sake of simplicity? – IMeasy Oct 14 at 18:28

kapranov’s realization of $\overline{M}_{0,n}$ over other fields

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kapranov’s realization of $\overline{M}_{0,n}$ over other fields

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