Mori dream spaces are algebraic varieties with finitely generated Cox ring; basic examples are toric varieties or rational varieties with a torus action of complexity one. Due to the finite generation of the Cox ring, Mori dream spaces allow an explicit approach in terms of commutative algebra an...
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...
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 ...