SCHOOL (AND WORKSHOP) ON THE
MINIMAL MODEL PROGRAM AND SHOKUROV'S ACC CONJECTURE
TRENTO, JULY 5-10, 2010
S. Boucksom (Universite de Paris VII, Fr) T. de Fernex (University of Utah, USA)
General informations on the School and Workshop.
The School/Workshop is organized by G. Casnati, M. Mella, R. Notari, G. Pacienza. For contacting the organizers send a mail to
The School/Workshop is supported by CIRM-Fondazione Bruno Kessler
(formerly CIRM-ITC), by GDRE-GRIFGA financed by INdAM and CNRS and by
The School and the Workshop will take place at
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.
Aim of Workshop.
The Workshop is intended to discuss the state of the art. Up to now the following speakers have confirmed their participation: C. Casagrande, F. Catanese, I. Cheltsov, V. Lazic, G. Occhetta. People interested in delivering a short communication are kindly requested to submit the title and an abstract within June 21st to
The School will start on Monday, 5th at 13.00 and it will end on Friday, 9th at 12.30. Workshop will start on Friday 9th at 14.30 and it will end on Saturday 10th at 14.00. On Friday evening a social dinner open to the participants of the School/Workshop will be organized.
Financial supports for Participants.
There are some grants covering lodging expenses in double rooms for young participants. Applicants must fill in the online application form before May, 29th. The organizing commitee will examine the applications and will send out notifications of acceptance by June 14th.
Participants who do not require financial support are expected to fill in the on line registration form before June 21st.
A third announcement will follow, probably in May.