|
|
 Winter school on Birational geometry
Les Diablerets, January 24-28, 2011
The winter school was held in Les Diablerets (Switzerland) from January 24 to 28, 2011.
Courses and Schedule
Each morning from 9:00 to 12:30, there were three mini-courses, each of one hour:
|
An introduction to birational geometry of surfaces |
Jérémy Blanc |
Basel |
|
An introduction to automorphisms with positive entropy
on compact complex surfaces |
Julie Déserti |
Paris 7 / Basel |
|
Minimal model program and factorization of birational maps |
Stéphane Lamy |
Warwick / Lyon 1 |
(for the abstracts, see below).
The lunch was at 12:30, and then participants had time to think about the exercises. In the afternoon, exercise session for questions / discussions were from 16:45 to 19:45.
Location
The conference was held at the
Hôtel Les Sources, Les Diablerets, Switzerland.
Participants
Supported by Swiss doctoral program:
Peter Feller (Bern), Yi-Ning Hsiao (Genève), Alexander Kolpakov (Fribourg), Matthias Leuenberger (Bern), Lionel Lang (Genève), Filip Misev (Basel), Daniel Arnold Moldovan (Lausanne), Aglaia Myropolska (Genève), Maria Fernanda Robayo (Basel), Kristin Shaw (Genève), Immanuel Stampfli (Basel)
Other participants:
Emilie Dufresne (Basel), Seung-Jo Jung (Warwick), Pierre-Marie Poloni (Basel), Johannes Rau (Genève), Michael Selig (Warwick)
Support
The Swiss Doctoral Program in Mathematics was able to cover food, lodging and travel expenses of participants which are PhD students and belong to the program ; a participation of 150 CHF was required for the full pension.
Support for this conference was provided by the Swiss Doctoral Program in Mathematics.
Abstracts
|
An introduction to birational geometry of surfaces - J. Blanc
In this lectures, I would like to explain some very basic notions of birational geometry, focusing on projective surfaces and trying to avoid as much possible the technical things.
I will explain what is a blow-up of a point on a smooth surface, and will talk about exceptional curves, self-intersection, linear systems, divisors, ... Many examples will be given, and links between del Pezzo surfaces will be discussed, for example showing the classical well-known fact that a cubic surface is the blow-up of 6 points in the projective plane, and how to recover the 27 lines on the surfaces by this blow-up.
Informal notes
|
|
An introduction to automorphisms with positive entropy on compact complex surfaces - J. Déserti
We will deal with automorphisms of positive entropy, that is roughly speaking automorphisms with a chaotic behavior, on rational surfaces.
After seeing that such automorphisms exist on some very particular surfaces, we will give a way to construct some.
Informal notes
|
|
Minimal model program and factorization of birational maps - S. Lamy
Given a birational map, say from P^3 to P^3, the Sarkisov program aims
at producing a factorization of this map by means of so-called
elementary links.
In a recent preprint [HMcK] C. Hacon and J. McKernan obtain a proof of
the Sarkisov program in arbitrary dimension, as a corollary of results
from the already cult paper [BCHM], which essentially establishes the
Minimal Model Program in any dimension.
In these lectures, I plan to take [HMcK] as a pretext to introduce some
material from the MMP. I hope I can make the audience understand the
meaning of one or two crucial statements (not proofs !) from [BCHM],
explain the novelties of [HMcK] from the previous work by Corti [C], and
work out some easy concrete examples.
|
[BCHM] | C. Birkar, P. Cascini, C. Hacon and J. McKernan, Existence of
minimal models for varieties of log general type, J. Amer. Math. Soc.,
vol 23, 405-468, 2010. | |
[C] | A. Corti, Factoring birational maps of threefolds after Sarkisov, J.
Algebraic Geom, 4, 223--254, 1995. | |
[HMcK] | C. Hacon and J. McKernan, The Sarkisov program, arXiv:0905.0946. | |
[M] | K. Matsuki, Introduction to the Mori program. Universitext,
Springer-Verlag, 2002. |
Informal notes
|
|