| 概要 | Mori dream space (MDS), introduced by Y. Hu and S. Keel, is a class of varieties which can be regarded as a generalization of log Fano varieties. At the same time MDS is the class of varieties whose geometry can be identified with the VGIT of the Cox ring.
In my talk I prove that the image of a morphism from a MDS again is a MDS. Then I introduce a fan structure on the effective cone of a MDS and show that the fan of the image coincides with the restriction of that of the source. This fan encodes some information of the Zariski decompositions, which turns out to be equivalent to the information of so called GIT equivalence. The point is that these results can be clearly explained via the VGIT description for MDS.
If I have time, I touch on generalizations and an application to the Shokurov polytopes. |