Algebra & Number Theory
- Algebra Number Theory
- Volume 4, Number 7 (2010), 855-885.
Equations for Chow and Hilbert quotients
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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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)
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