Let X be a smooth Mori dream space of dimension ≥ 4. We show that, if X satisfies a suitable GIT condition which we call small unstable locus , then every smooth ample divisor Y of X is also a Mori dream space. Moreover, the restriction map identifies the Néron–Severi spaces of X...
1. Introduction Mori dream spaces, which were introduced by Hu and Keel in [4], are special vari- eties which have very nice properties in view of the minimal model program. In the paper, Hu and Keel investigated properties of Mori dream spaces, especially those related to GIT. We ...
Mori dream spacesWe propose an algorithm to compute the GIT-fan for torus actions on affine varieties with symmetries. The algorithm combines computational techniques from commutative algebra, convex geometry, and group theory. We have implemented our algorithm in the S INGULAR library GITFAN.LIB ....
We link small modifications of projective varieties with a ${\\mathbb C}^*$-action to their GIT quotients. Namely, using flips with centers in closures of Bia{\\l}ynicki-Birula cells, we produce a system of birational equivariant modifications of the original variety, which includes those ...
Small modifications of Mori dream spaces arising from \\(\\mathbb {C}^*\\)-actionsTorus actionsBirational geometryWe link small modifications of projective varieties with a \\({\\mathbb {C}}^*\\)-action to their GIT quotients. Namely, using flips with centers in closures of Biaynicki-Bi...