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...
We prove that the moduli space of n n -pointed stable maps \overline{M}_{0,n}(\mathbb{P}^1,1) \overline{M}_{0,n}(\mathbb{P}^1,1) is a Mori dream space whenever the moduli space \overline{M}_{0,n+3} \overline{M}_{0,n+3} of (n+3) (n+3) -pointed rational cur...
We prove that a GIT chamber quotient of an affine variety $X=Spec(A)$ by a reductive group $G$, where $A$ is an almost factorial domain, is a Mori dream space if it is projective, regardless of the codimension of the unstable locus. This includes an explicit description of the ...
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 ...
varieties with a Cdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${mathbb {C}}^*$$end{document}-action to their GIT ...