Jérémy Blanc - Universität Basel - Mathematik
  Conference in algebraic geometry - "Birpol3"
Basel, November 28-30, 2012
The conference will be held in Basel from November 28 to 30, 2012.

Hanspeter KRAFT
Stéphane LAMY
Freiburg in Brisgau

November 28
November 29
November 30
  in Rheinsprung 21
Grosse Hörsaal:

 Singular quartic 3-folds
and Sarkisov links

 coffee break

 Hanspeter KRAFT
 Varieties Characterized
by their Endomorphims
in Rheinsprung 21
Grosse Hörsaal:

 Affine T-varieties of complexity
one over an arbitrary field.

 coffee break
 Singular spaces with
trivial canonical class
 Welcome in Rheinsprung 21

in Alte Universität
Rheinsprung 9 /11, Raum 118:

 Stéphane LAMY
 On the genus of birational
selfmaps of 3, after Frumkin

 coffee break

 Invariants and Separating
morphisms for algebraic
group actions

in Rheinsprung 21
Grosse Hörsaal:


 A description of certain affine
hyperbolic *-varieties
of complexity two.


 coffee break

 Deformations of rational
surface automorphisms
 Social dinner

Hamid AHMADINEZHAD - Singular quartic 3-folds and Sarkisov links
Quartic 3-folds with terminal singularities are among the simplest Fano varieties in three dimensions, yet their geometry is not well understood. In this talk I report on a work in progress, joint with Anne-Sophie Kaloghiros, which studies possible birational models of these objects. Sarkisov links via Cox rings of rank two are the natural method to tackle this problem. Some examples are explicitly described during the talk to illustrate this technique.
Emilie DUFRESNE - Invariants and Separating morphisms for algebraic group actions
We study the invariants of an algebraic group action on an affine variety via separating morphisms, that is, dominant G-invariant morphism to another affine variety such that points which are separated by some invariant have distinct image. This is a more geometric take on the study of separating invariants, a new trend in invariant theory initiated by Derksen and Kemper. In this talk, I will discuss some results which indicate that the fact that the invariants are not always finitely generated is less significant than the fact that what we would want to call the quotient morphism is not always surjective.

Joint work with Hanspeter Kraft.
Julien GRIVAUX - Deformations of rational surface automorphisms
Although difficult to construct, rational surface automorphisms can occur in arbitrary large holomorphic families. In this talk, we will explain how the classical theory of deformations of complex manifolds of Kodaira and Spencer can be used to study deformations of rational surface automorphisms.
Stefan KEBEKUS - Singular spaces with trivial canonical class
The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, and irreducible, simply-connected Calabi-Yau-- and holomorphic-symplectic manifolds. The decomposition of the simply-connected part corresponds to a decomposition of the tangent bundle into a direct sum whose summands are integrable and stable with respect to any polarisation. Building on recent extension theorems for differential forms on singular spaces, we prove an analogous decomposition theorem for the tangent sheaf of projective varieties with canonical singularities and numerically trivial canonical class. In view of recent progress in minimal model theory, this result can be seen as a first step towards a structure theory of manifolds with Kodaira dimension zero. Based on our main result, we argue that the natural building blocks for any structure theory are two classes of canonical varieties, which generalise the notions of irreducible Calabi-Yau-- and irreducible holomorphic-symplectic manifolds, respectively.
  This is joint work with Daniel Greb and Thomas Peternell.
Hanspeter KRAFT - Varieties Characterized by their Endomorphims
I will explain the following astonishing result: If two varieties X and Y have isomorphic endomorphism semigroups and if one of them is affine and contains a copy of the affine line, then X and Y are isomorphic up to base change. The proof is based on some classical results of Dick Palais and uses tools from algebraic geometry and algebraic transformation groups.
  Joint work with Rafael Andrist.
Stéphane LAMY - On the genus of birational selfmaps of 3, after Frumkin
В работе вводится понятие рода бирационального отображения неособых трехмерных алгебраических многообразий над полем характеристики 0 и доказывается, что автоморфизмы рода не больше фиксированного образуют группу. В работе доказано, что бирациональный морфизм трехмерных неособых многообразий разлагается в композицию отображения, обратного морфизму рода 0, и моноидальных преобразований. link
Kevin LANGLOIS -Affine T-varieties of complexity one over an arbitrary field.
In this talk, we will explain that the presentation of an affine T-variety of complexity one in terms of polyhedral divisors holds over an arbitrary field.
Charlie PETITJEAN - A description of certain affine hyperbolic C*-varieties of complexity two.
The complexity of a T-variety X is defined to be the minimal codimension of the T-orbits in X. A variety toric is therefore a T-variety of complexity 0. Altmann and Hausen have given a more general description of T-affine varieties of any complexity, in terms of polyhedral divisors on quasi-projective varieties. In this talk, I will review this construction for a class of affine threefolds of complexity 2 with a C*-action , with particular focus on the Koras-Russell threefolds and certain hyperbolic modifications.

Hamid Ahmadinhezhad (Linz)
Bachar Al Hajjar (Dijon)
Cinzia Bisi (Ferrara)
Jérémy Blanc (Basel)
Julie Déserti (Basel)
Emilie Dufresne (Basel)
Adrien Dubouloz (Dijon)
Jean-Philippe Furter (La Rochelle)
Stéphane Lamy (Warwick)
Kevin Langlois (Grenoble)
Alvaro Liendo (Bern)
Lucy Moser-Jauslin (Dijon)
Shameek Paul (Dijon)
Charlie Petitjean (Dijon)
Alexander Perepechko (Grenoble)
Pierre-Marie Poloni (Basel)
Andriy Regeta (Basel)
Maria Fernanda Robayo (Basel)
Josef Schicho (Linz)
Immanuel Stampfli (Basel)
Mikhail Zaidenberg (Grenoble)

Financial support
We gratefully acknowledge support from:
Swiss national Science Foundation and
French ANR Birpol