We give explicit equations for the Chow and Hilbert quotients of a projective scheme by the action of an algebraic torus in an auxiliary toric variety. As a consequence we provide geometric invariant theory descriptions of these canonical quotients, and obtain other GIT quotients of by variation of GIT quotient. We apply these results to find equations for the moduli space of stable genus-zero -pointed curves as a subvariety of a smooth toric variety defined via tropical methods.
"Equations for Chow and Hilbert quotients." Algebra Number Theory 4 (7) 855 - 885, 2010. https://doi.org/10.2140/ant.2010.4.855