# Mori program for Brauer pairs in dimension three

July 14 to July 18, 2014

at the

American Institute of Mathematics, Palo Alto, California

organized by

Daniel Chan, Kenneth Chan, Colin Ingalls, and Sandor Kovacs

## Original Announcement

This workshop will be devoted to the Mori program for Brauer log pairs in dimension three.

The recent proof of the finite generation of the canonical ring is a major milestone in the Mori program for classifying higher dimensional varieties. The framework of the Mori program has been established in many different contexts, such as for log varieties, varieties with group actions, and rather surprisingly, for Brauer log pairs. These pairs arise naturally in the study of maximal orders and generic projective space bundles. The Mori program in the context of Brauer log pairs, which we call Brauer log MMP, has been completed in dimension two. The main focus for this workshop is to extend this work to dimension three and explore some applications.

The main topics for the workshop are

• Existence of terminal resolutions.
The notion of discrepancy generalises for Brauer log pairs, so we can define Brauer terminal pairs. Does every Brauer log pair admit a terminal resolution?

• Mori contractions.
What properties of a Brauer terminal pair are preserved under Mori contractions?
What is the right definition of a flip for Brauer log pairs?

• Classification of terminal pairs and étale local models.
Classify the ramification data associated to Brauer log pairs which are Brauer terminal.
Given a maximal order on a threefold germ $X$, we can associate a Brauer log pair. If we fix a Brauer log pair $(X,\alpha)$ which is Brauer terminal, can we classify the maximal orders such that the associated Brauer log pair is $(X,\alpha)$?

## Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.