TRENTO, JULY 5-10, 2010

First announcement


S. Boucksom (Universite de Paris VII, Fr)
T. de Fernex (University of Utah, USA)

The School/Workshop is organized by G. Casnati, M. Mella, R. Notari, G. Pacienza. For contacting the organizers send a mail to

geometri [nospam]

Aim of the School.
The School is mainly aimed to Phd students and young researchers in Algebraic Geometry, introducing the participants to research, beginning from a basic level with a view towards the applications and to the most recent results.
S. Boucksom. The Minimal Model Program was initiated in the early eighties by Kawamata, Mori, Reid, Shokurov as an attempt to extend the birational classification of surfaces to higher dimensions. The primary goal of these lectures will be to present the fundamental tools in question, that is the type of singularities one has to deal with, the non-vanishing theorem, the cone theorem and the contraction theorem. Much more recently, tremendous progress has been achieved by the joint efforts of several people. The existence of flips has been established as well as a certain kind of termination, which is good enough to get the existence of minimal models for varieties of general type. Some aspects of these developments will be discussed.
T. de Fernex. After the recent  breakthrough in the Minimal Model Program, one of the few parts that is still missing in the program is the Termination of Flips Conjecture. It turns out that this conjecture is related to some subtle property of the singularities involved encoded in a conjecture by Shokurov. These series of lectures are devoted to an overview of this problem and a discussion of some recent progress in this direction. After briefly presenting the motivation, the attention will be focused on log canonical thresholds, discussing their basic properties and proceeding through the proofs of the results that have been obtained towards Shokurov's ACC Conjecture.

Further announcements.
A more detailed second announcement (containing informations on accomodation, registration and financial supports) will follow probably in February 2010.