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arXiv · 1805.10925

On Mori chamber and stable base locus decompositions

Antonio Laface·Alex Massarenti·Rick Rischter
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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.

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Antonio Laface, Alex Massarenti, Rick Rischter. 2018-05-28. On Mori chamber and stable base locus decompositions. https://arxiv.org/abs/1805.10925

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