Algebra & Number Theory

Equations for Chow and Hilbert quotients

Angela Gibney and Diane Maclagan

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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.

Article information

Algebra Number Theory, Volume 4, Number 7 (2010), 855-885.

Received: 29 May 2009
Revised: 17 February 2010
Accepted: 5 May 2010
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14L24: Geometric invariant theory [See also 13A50] 14H10: Families, moduli (algebraic)

Chow quotient Hilbert quotient moduli of curves space of phylogenetic trees


Gibney, Angela; Maclagan, Diane. Equations for Chow and Hilbert quotients. Algebra Number Theory 4 (2010), no. 7, 855--885. doi:10.2140/ant.2010.4.855.

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