Mori dream space
In algebraic geometry, a Mori dream space is a projective variety whose cone of effective divisors has a well-behaved decomposition into certain convex sets called "Mori chambers".[1] Hu and Keel showed that Mori dream spaces are quotients of affine varieties by torus actions.[1] The notion is named so because it behaves nicely from the point of view of Mori's minimal model program.
Examples and Properties
Any quasi-smooth projective spherical variety (in particular, any quasi-smooth projective toric variety) as well as any log Fano 3-fold is a Mori dream space.[1] In general, it is difficult to find a non-trivial example of a Mori dream space, as being a Mori Dream Space is equivalent to all (multi-)section rings being finitely generated.[2]
It has been shown that a variety which admits a surjective morphism from a Mori dream space is again a Mori dream space.[3]
See also
References
- ↑ 1.0 1.1 1.2 Hu, Yi; Keel, Sean (2000). "Mori dream spaces and GIT". The Michigan Mathematical Journal 48 (1): 331–348. doi:10.1307/mmj/1030132722. ISSN 0026-2285.
- ↑ Castravet, Ana-Maria (2018). "Mori dream spaces and blow-ups". Proceedings of Symposia in Pure Mathematics 97 (1). http://dx.doi.org/10.1090/pspum/097.1/01671.
- ↑ Okawa, Shinnosuke (2016). "On images of Mori dream spaces". Mathematische Annalen 364 (3-4): 1315–1342. doi:10.1007/s00208-015-1245-5.
 |  |
