On Kapranov's description of M_{0,n} as a Chow quotient

Details On Kapranov's description of M_{0,n} as a Chow quotient On Kapranov's description of M_{0,n} as a Chow quotient

2011-03-24

arxiv.org/abs/1103.4661v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

We provide a direct proof, valid over the integers, of the result originally proven by Kapranov that the Hilbert and Chow quotients P1^n//PGL2 are isomorphic to \bar{M}_{0,n}. In both cases this is done by explicitly constructing the universal family and then showing that the induced morphism is an isomorphism onto its image. The proofs of these results in many ways reduce to the case n = 4; in an appendix we outline a formalism of this phenomenon relating to certain operads.

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