On Kapranov's description of \overline{M}0,n as a Chow quotient

Authors : Noah Giansiracusa, William Danny Gillam

Pages : 625-648

Doi:10.3906/mat-1306-17

View : 16 | Download : 13

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :We provide a direct proof, valid in arbitrary characteristic, of the result originally proven by Kapranov over C that the Hilbert quotient (P1)n//HPGL2 and Chow quotient (P1)n//ChPGL2 are isomorphic to \overline{M}0,n. In both cases this is done by explicitly constructing the universal family of orbit closures 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.
Keywords : Chow quotient, Hilbert quotient, moduli of curves, configuration of points