Equations for Chow and Hilbert quotients
By A. Gibney, Diane Maclagan. 2007
65 citations recorded by the source corpus.
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) over bar (0,n) of stable genus-zero n-pointed curves as a subvariety of a smooth toric variety defined via tropical methods.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6cc1d048bd892514077593d0eabc8fec5ae2d8e5
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In Computational Theory and Mathematics
- Dhruv Ranganathan
- Renzo Cavalieri
- Ana-Maria Castravet
- Simon Hampe
- Jenia Tevelev
- Hannah Markwig
- Martin Ulirsch
- G. Mikhalkin
In Geometry and Topology
- Dhruv Ranganathan
- Renzo Cavalieri
- Hannah Markwig
- Simon Hampe
- Ana-Maria Castravet
- Jenia Tevelev
- Martin Ulirsch
- Bernd Sturmfels
Citations in the corpus
- MODULI SPACES OF RATIONAL WEIGHTED STABLE CURVES AND TROPICAL GEOMETRY (2014, result): “Then we have the following result, due to Gibney and Maclagan [GM, Theorem 5.7], as well as Tevelev [T1, Theorem 5.5] Theorem 2.1.”
- $\overline{M}_{0,n}$ is not a Mori Dream Space (2013, background): “ro, log-Fano varieties are MDS by [BCHM10]; however, M0,n is not log-Fano for n ≥ 7). Since [HK00], the question whether M0,n is a MDS was raised by several authors, see for example [Cas09], [AGS10], [GM10], [McK10], [Fed11], [BHK12], [GG12], [GHPS12], [GM12], [BGM13], [CT13], [GJM13], [Lar13]. One ”
- Tropical intersection theory from toric varieties (2009, unknown): “A G ] 1 5 Ju l 2”