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

Authors

NOAH GIANSIRACUSA
WILLIAM DANNY GILLAM

DOI

10.3906/mat-1306-17

Abstract

We provide a direct proof, valid in arbitrary characteristic, of the result originally proven by Kapranov over C that the Hilbert quotient (P^1)^n//_HPGL_2 and Chow quotient (P^1)^n//_{Ch}PGL_2 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

First Page

625

Last Page

648

Recommended Citation

GIANSIRACUSA, NOAH and GILLAM, WILLIAM DANNY (2014) "On Kapranov's description of \overline{M}_{0,n} as a Chow quotient," Turkish Journal of Mathematics: Vol. 38: No. 4, Article 3. https://doi.org/10.3906/mat-1306-17
Available at: https://journals.tubitak.gov.tr/math/vol38/iss4/3