On the Mori theory and NewtonOkounkov bodies of BottSamelson varieties
Abstract
We prove that on a BottSamelson variety $X$ every movable divisor is nef. This enables us to consider Zariski decompositions of effective divisors, which in turn yields a description of the Mori chamber decomposition of the effective cone. This amounts to information on all possible birational morphisms from $X$. Applying this result, we prove the rational polyhedrality of the global NewtonOkounkov body of a BottSamelson variety with respect to the so called `horizontal' flag. In fact, we prove the stronger property of the finite generation of the corresponding global value semigroup.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 DOI:
 10.48550/arXiv.1709.09910
 arXiv:
 arXiv:1709.09910
 Bibcode:
 2017arXiv170909910M
 Keywords:

 Mathematics  Algebraic Geometry;
 14C20;
 14L30
 EPrint:
 28 pages, added results about NewtonOkounkov bodies and the global value semigroup