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(Sep. 6) Separating Mori chambers by base schemes

Last updated :2019-09-04

Topic: Separating Mori chambers by base schemes
Speaker: Associate Professor Shin-Yao Jow
(Taiwan Tsing Hua University)
Time: 16:00-17:00, Friday, September 6, 2019
Venue: Room 416, Mathematics Building, Guangzhou South Campus, SYSU

Abstract:
Mori dream spaces are a class of projective varieties whose birational geometry can be described in terms of combinatorial data.

They are introduced by Hu and Keel, and include toric varieties and Fano varieties as examples. The effective cone of a Mori dream space can be decomposed into finitely many rational polyhedral subcones, called Mori chambers, which are characterized by the property that two divisors are in the interior of the same Mori chamber if and only if they define the same Iitaka fibration.

It is known that divisors in the interiors of different Mori chambers may have the same stable base locus. Here we show, however, that they cannot have the same "stable base scheme". A toric example will be given to illustrate our result, where a "flip of embedded components" occurs to the base scheme of a divisor when it crosses the wall between two Mori chambers.