On existence of log minimal models and weak Zariski decompositions

Details On existence of log minimal models and weak Zariski decompositions On existence of log minimal models and weak Zariski decompositions

2009-07-29

arxiv.org/abs/0907.5182v1

Mathematics

Algebraic Geometry

Scientific paper

We first introduce a weak type of Zariski decomposition in higher dimensions: an $\R$-Cartier divisor has a weak Zariski decomposition if birationally and in a numerical sense it can be written as the sum of a nef and an effective $\R$-Cartier divisor. We then prove that there is a very basic relation between Zariski decompositions and log minimal models which has long been expected: we prove that assuming the log minimal model program in dimension $d-1$, a lc pair $(X/Z,B)$ of dimension $d$ has a log minimal model if and only if $K_X+B$ has a weak Zariski decomposition$/Z$.

Affiliated with

Also associated with

No associations

Rating

On existence of log minimal models and weak Zariski decompositions 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 On existence of log minimal models and weak Zariski decompositions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On existence of log minimal models and weak Zariski decompositions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-522152