## Algebra & Number Theory

### Equations for Chow and Hilbert quotients

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ant/1513729587

Digital Object Identifier
doi:10.2140/ant.2010.4.855

Mathematical Reviews number (MathSciNet)
MR2776876

Zentralblatt MATH identifier
1210.14051

#### Citation

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. https://projecteuclid.org/euclid.ant/1513729587

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