Mori Dream Spaces and GIT

Details Mori Dream Spaces and GIT Mori Dream Spaces and GIT

2000-04-04

arxiv.org/abs/math/0004017v1

Mathematics

Algebraic Geometry

Scientific paper

The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call such a variety a Mori Dream Space. There turn out to be many examples, including quasi-smooth projective toric (or more generally, spherical) varieties, many GIT quotients, and log Fano 3-folds. We characterize Mori dream spaces as GIT quotients of affine varieties by a torus in a manner generalizing Cox's construction of toric varieties as quotients of affine space. Via the quotient description, the chamber decomposition of the cone of divisors in Mori theory is naturally identified with the decomposition of the G-ample cone from geometric invariant theory. In particular every rational contraction of a Mori dream space comes from GIT, and all possible factorizations of a rational contraction can be read off from the chamber decomposition.

Affiliated with

Also associated with

No associations

Rating

Mori Dream Spaces and GIT does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mori Dream Spaces and GIT, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mori Dream Spaces and GIT will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-73208