Vol. 4, No. 7, 2010

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Equations for Chow and Hilbert quotients

Angela Gibney and Diane Maclagan

Vol. 4 (2010), No. 7, 855–885

We give explicit equations for the Chow and Hilbert quotients of a projective scheme X by the action of an algebraic torus T in an auxiliary toric variety. As a consequence we provide geometric invariant theory descriptions of these canonical quotients, and obtain other GIT quotients of X by variation of GIT quotient. We apply these results to find equations for the moduli space M¯0,n of stable genus-zero n-pointed curves as a subvariety of a smooth toric variety defined via tropical methods.

Chow quotient, Hilbert quotient, moduli of curves, space of phylogenetic trees
Mathematical Subject Classification 2000
Primary: 14L30
Secondary: 14M25, 14L24, 14H10
Received: 29 May 2009
Revised: 17 February 2010
Accepted: 5 May 2010
Published: 29 January 2011
Angela Gibney
Department of Mathematics
University of Georgia
Athens, GA 30602
United States
Diane Maclagan
Mathematics Institute
Zeeman Building
University of Warwick
United Kingdom