Groups of Automorphisms in

Birational and Affine Geometry

Bellavista Relax Hotel, Levico Terme (Trento), Italy

October November 3.rd, 2012


Lago di Levico, veduta autunnale - Fototeca Trentino SPA – Foto Flavio Faganello



Scientific Committee

·         Ivan Cheltsov (U. Edinburgh)

·         Ciro Ciliberto (U. Roma Tor Vergata)

·         Hubert Flenner (U. Bochum)

·         James McKernan (MIT Boston)

·         Yuri Prokhorov (Moscow U.)

·         Mikhail Zaidenberg (Inst. Fourier, Grenoble)

Objectives of the Conference

The subject of the conference includes: Studies on groups of automorphisms of affine and projective algebraic varieties, birational transformation groups, and related geometry. The problem of describing the automorphism groups of both affine or projective algebraic varieties is a classical subject in algebraic geometry. It is commonly accepted that the affine case is substantially more complicated than the projective one, while it is rather close to the setting of the birational geometry. In both cases the groups in question are often infinite dimensional, while the groups of biregular automorphims of a projective variety are close to algebraic, in particular, they are finite dimensional. However, the automorphism group of an affine variety, even if it can be infinite dimensional, carries some similarity with an algebraic group. Meanwhile the automorphism group are completely known only for a rather narrow class of varieties.

For a long time, the dominant tendency in the development of both affine and projective geometry was divergence of their interests, of their main problems and methods. The organizers of the meeting would like to fight this tendency, to develop further the points of common interest, and the methods that work both in the affine and projective setting. The meeting should allow to look on its subjects from different perspectives.

As a technical tool which can be useful in both domains we can mention the Mori Theory and, more concretely, the Sarkisov Program. The latter provides an algorithm for decomposing any birational morphism of projective varieties of negative Kodaira dimension into a sequence of elementary ones. It works well for studying groups of birational automorphims (Iskovskikh, Corti, Cheltsov, e.a.). Recently, this program was successfully applied to some problems of affine geometry (Kishimoto, Dubouloz, Lamy). On the other hand, the Sarkisov program in its present state is rather non-effective. For its effective application one needs to know the concrete form of all the intermediate elementary birational transformations (Sarkisov links). The current work in this direction (Mori, Kawamata, Corti, Kawakita, Prokhorov, Blanc, Lamy e.a.) is far from being finished.


Click here to see the program and here the list of confirmed speakers and abstracts of the talks.

The Scientific Committee decided to have a poster session too, both in this web page and, during the conference, on paper posters. Participants interested in presenting a poster are invited to submit a .pdf-file (papers or abstracts, or links to other sources) to the e-mail address of the Secretary of CIRM Then, starting with the morning of Monday Oct. 29th, interested participants should post their posters on the poster-panels. The available board area for poster presentations is 100 cm (width) x 200 cm (height). The authors must provide their own printout of the title, authors and poster itself. Scotch tape and the session paper designation sign will be provided by the Conference staff.


Confirmed Participants

Click here to see the list.


For registering in the conference please complete and submit our registration form to the Secretary of CIRM.

No registration fee will be charged.

Deadline for registration: October 15th, 2012.

Logistic Information

Participants who need a paper-official invitation for obtaining visa to enter in Italy should contact the Secretary of CIRM.

The conference will be held in the conference hall of the Bellavista Relax Hotel in Levico Terme (Trento). Participants will be lodged in the same hotel. Arrival day is Sunday, October 28th  in the afternoon/evening. Lectures will start in the morning of Monday, October 29th  and end on Saturday, November 3rd after the lunch. Departure day is Saturday, November 3rd  after lunch.

The cost for the full board at Bellavista Relax Hotel is:

·         80,00 EUR per night in a single bedroom,

·         63,00 EUR per night per person in a double bedroom.

Please click here to find Information to reach Levico Terme and the conference site.



·         CIRM – Fondazione Bruno Kessler

·         DFG

·         GDR GAG (“Géométrie Algébrique et Géométrie Complete”)

·         GDR TLAG3 (“Théorie de Lie Algébrique et Géométrique”)

·         GDR “Singularités et Applications

·         ANR BirPol (Project JCJC “Automorphismes Polynomiaux et Transformations Birationnelles”)

·         UJF (Université Joseph Fourier, Grenoble I)

·         Institut Fourier de Mathématiques, Laboratoire de CNRS (Grenoble)

·         GDRE GRIFGA  (Groupement de Recherche européen Italo-Français en Géométrie Algébrique)

·         GRIFGA (Gruppo di Ricerca Italo-Francese in Geometria Algebrica)

·         Ministère de l’Enseignement Supérieur et de la Recherche (France)