Mori dream spaces and GIT.

@article{Hu2000MoriDS,
  title={Mori dream spaces and GIT.},
  author={Y. Hu and S. Keel},
  journal={Michigan Mathematical Journal},
  year={2000},
  volume={48},
  pages={331-348}
}
  • Y. Hu, S. Keel
  • Published 4 April 2000
  • Mathematics
  • Michigan Mathematical Journal
The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call such a variety a Mori Dream Space. There turn out to be many examples, including quasi-smooth projective toric (or more generally, spherical) varieties, many GIT quotients, and log Fano 3-folds. We characterize Mori dream spaces as GIT quotients of affine varieties by a torus in a manner generalizing… 
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