On Mori chamber and stable base locus decompositions |
| Antonio Laface |
| Universidad de Concepción |
| Abstract: |
| The effective cone of a Mori dream space [2] admits two decompositions into chambers called Mori chambers and stable base locus chambers (these are not necessarily convex cones). The former decomposition is a refinement of the latter, because Mori equivalent divisors have the same stable base locus. In this talk I will discuss both decompositions from a combinatorical viewpoint using the language of Cox rings [1, \[\S 3.3\] ] and provide examples when the two are different. At the end I will state a criterion to establish whether the two decompositions coincide for a Mori dream space of Picard rank two. |
| This is joint work [3] with A. Massarenti and R. Rischter. |
| References |
| [1] Ivan Arzhantsev, Ulrich Derenthal, Jürgen Hausen, and Antonio Laface, Cox rings, Cambridge Studies in Advanced Mathematics, vol. 144, Cambridge University Press, Cambridge, 2015. |
| [2] Yi Hu and Sean Keel, Mori dream spaces and GIT, Michigan Math. J. 48 (2000), 331–348. |
| [3] Antonio Laface, Alex Massarenti, and Rick Rischter, On Mori chamber and stable base locus decompositions. arXiv:1805.10925. |