On Mori chamber and stable base locus decompositions
Abstract
The effective cone of a Mori dream space admits two wall-and-chamber decompositions called Mori chamber and stable base locus decompositions. In general the former is a non trivial refinement of the latter. We investigate, from both the geometrical and the combinatorial viewpoints, the differences between these decompositions. Furthermore, we provide a criterion to establish whether the two decompositions coincide for a Mori dream space of Picard rank two, and we construct an explicit example of a Mori dream space of Picard rank two for which the decompositions are different, showing that our criterion is sharp. Finally, we classify the smooth toric 3-folds of Picard rank three for which the two decompositions are different.
Cite
@article{arxiv.1805.10925,
title = {On Mori chamber and stable base locus decompositions},
author = {Antonio Laface and Alex Massarenti and Rick Rischter},
journal= {arXiv preprint arXiv:1805.10925},
year = {2019}
}
Comments
26 pages. Added the classification of smooth toric 3-folds of Picard rank three for which the Mori chamber and the stable base locus decomposition differ. To appear in Transactions of the American Mathematical Society